Multi-Robot Motion Planning (MRMP) involves generating collision-free trajectories for multiple robots operating in a shared continuous workspace. While discrete multi-agent path finding (MAPF) methods are broadly adopted due to their scalability, their coarse discretization severely limits trajectory quality. In contrast, continuous optimization-based planners offer higher-quality paths but suffer from the curse of dimensionality, resulting in poor scalability with respect to the number of robots. This paper tackles the limitations of these two approaches by introducing a novel framework that integrates discrete MAPF solvers with constrained generative diffusion models. The resulting framework, called Discrete-Guided Diffusion (DGD), has three key characteristics: (1) it decomposes the original nonconvex MRMP problem into tractable subproblems with convex configuration spaces, (2) it combines discrete MAPF solutions with constrained optimization techniques to guide diffusion models capture complex spatiotemporal dependencies among robots, and (3) it incorporates a lightweight constraint repair mechanism to ensure trajectory feasibility. The proposed method sets a new state-of-the-art performance in large-scale, complex environments, scaling to 100 robots while achieving planning efficiency and high success rates.

Anytime multi-agent path finding (MAPF) is a promising approach to scalable and collision-free path optimization in multi-agent systems. MAPF-LNS, based on Large Neighborhood Search (LNS), is the current state-of-the-art approach where a fast initial solution is iteratively optimized by destroying and repairing selected paths, i.e., a neighborhood, of the solution. Delay-based MAPF-LNS has demonstrated particular effectiveness in generating promising neighborhoods via seed agents, according to their delays. Seed agents are selected using handcrafted strategies or online learning, where the former relies on human intuition about underlying structures, while the latter conducts black-box optimization, ignoring any structure. In this paper, we propose Truncated Adaptive Counterfactual K-ranked LEarning (TACKLE) to select seed agents via informed online learning by leveraging handcrafted strategies as human intuition. We show theoretically that TACKLE dominates its handcrafted and black-box learning counterparts in the limit. Our experiments demonstrate cost improvements of at least 60% in instances with one thousand agents, compared with state-of-the-art anytime solvers.

Multi-agent path finding (MAPF) is the challenging problem of finding conflict-free paths with minimal costs for multiple agents. While traditional MAPF solvers are centralized using heuristic search, reinforcement learning (RL) is becoming increasingly popular due to its potential to learn decentralized and generalizing policies. RL-based MAPF must cope with spatial coordination, which is often addressed by combining independent training with ad hoc measures like replanning and communication. Such ad hoc measures often complicate the approach and require knowledge beyond the actual accessible information in RL, such as the full map occupation or broadcast communication channels, which limits generalizability, effectiveness, and sample efficiency. In this paper, we propose Partitioned Attention-based Reverse Curricula for Enhanced Learning (PARCEL), considering a bounding region for each agent. PARCEL trains all agents with overlapping regions jointly via self-attention to avoid potential conflicts. By employing a reverse curriculum, where the bounding regions grow as the policies improve, all agents will eventually merge into a single coordinated group. We evaluate PARCEL in two simple coordination tasks and four MAPF benchmark maps. Compared with state-of-the-art RL-based MAPF methods, PARCEL demonstrates better effectiveness and sample efficiency without ad hoc measures.

Multi-objective search (MOS) has emerged as a unifying framework for planning and decision-making problems where multiple, often conflicting, criteria must be balanced. While the problem has been studied for decades, recent years have seen renewed interest in the topic across AI applications such as robotics, transportation, and operations research, eflecting the reality that real-world systems rarely optimize a single measure. This paper surveys developments in MOS while highlighting cross-disciplinary opportunities, and outlines open challenges that define the emerging frontier of MOS research.

In Bi-Objective Search (BOS), the task is to compute the Pareto-optimal frontier of paths in a graph with two cost values per edge. Recent work introduced a general BOS framework that classifies search nodes and studies how ordering functions affect expansion order. In this paper, we continue this line of research. We further refine the classes of nodes and show that many nodes that were added to the open list and are classified as never-expand nodes still need to be extracted and further examined. Additionally, we introduce a method that enables constant-time dominance checks for the MIN and MAX ordering functions. This allows a practical usage of these ordering functions, as we demonstrate in our experimental section.

Abstract A wide range of real-world applications can be formulated as Multi-Agent Path Finding (MAPF) problem, where the goal is to find collision-free paths for multiple agents with individual start and goal locations. State-of-the-art MAPF solvers are mainly centralized and depend on global information, which limits their scalability and flexibility regarding changes or new maps that would require expensive replanning. Multi-agent reinforcement learning (MARL) offers an alternative way of addressing MAPF problems by learning decentralized policies that can generalize over a variety of maps. While there exist some prior works that attempt to connect both areas, the proposed techniques are heavily engineered and very complex due to the integration of many mechanisms that limit generality and are expensive to use. We argue that much simpler and more general approaches are needed to bring the areas of MARL and MAPF closer together with significantly lower costs. In this paper, we propose Confidence-based Auto-Curriculum for Team Update Stability (CACTUS) as a lightweight MARL approach to MAPF. CACTUS defines a simple reverse curriculum scheme, where the goal of each agent is randomly placed within an allocation radius around the agent's start location. The allocation radius increases gradually as all agents improve, which is assessed by a confidence-based measure. In addition, we propose an extension called Confidence- and Conflict-Based Curriculum Learning with Allocation Radius Adaptation (C3LARA), using weighted sampling of goal locations to improve conflict resolution in scenarios of high agent density. We provide a theoretical analysis of the strengths and limitations of CACTUS regarding exploration efficiency and multi-agent coordination. We evaluate CACTUS and C3LARA in various maps of different sizes, obstacle densities, and numbers of agents. Our experiments demonstrate better performance and generalization capabilities than state-of-the-art MARL approaches with less than 600,000 trainable parameters, which is less than 5% of the neural network size of current MARL approaches to MAPF.

Monte-Carlo Tree Search (MCTS) is a popular approach to online planning under uncertainty. While MCTS uses statistical sampling via multi-armed bandits to avoid exhaustive search in complex domains, common closed-loop approaches typically construct enormous search trees to consider a large number of potential observations and actions. On the other hand, open-loop approaches offer better memory efficiency by ignoring observations but are generally not competitive with closed-loop MCTS in terms of performance - even with commonly integrated human knowledge. In this paper, we propose Counterfactual Open-loop Reasoning with Ad hoc Learning (CORAL) for open-loop MCTS, using a causal multi-armed bandit approach with unobserved confounders (MABUC). CORAL consists of two online learning phases that are conducted during the open-loop search. In the first phase, observational values are learned based on preferred actions. In the second phase, counterfactual values are learned with MABUCs to make a decision via an intent policy obtained from the observational values. We evaluate CORAL in four POMDP benchmark scenarios and compare it with closed-loop and open-loop alternatives. In contrast to standard open-loop MCTS, CORAL achieves competitive performance compared with closed-loop algorithms while constructing significantly smaller search trees.

Anytime multi-agent path finding (MAPF) is a promising approach to scalable and collision-free path optimization in multi-agent systems. MAPF-LNS, based on Large Neighborhood Search (LNS), is the current state-of-the-art approach where a fast initial solution is iteratively optimized by destroying and repairing selected paths of the solution. Current MAPF-LNS variants commonly use an adaptive selection mechanism to choose among multiple destroy heuristics. However, to determine promising destroy heuristics, MAPF-LNS requires a considerable amount of exploration time. As common destroy heuristics are stationary, i.e., non-adaptive, any performance bottleneck caused by them cannot be overcome by adaptive heuristic selection alone, thus limiting the overall effectiveness of MAPF-LNS. In this paper, we propose Adaptive Delay-based Destroy-and-Repair Enhanced with Success-based Self-learning (ADDRESS) as a single-destroy-heuristic variant of MAPF-LNS. ADDRESS applies restricted Thompson Sampling to the top-K set of the most delayed agents to select a seed agent for adaptive LNS neighborhood generation. We evaluate ADDRESS in multiple maps from the MAPF benchmark set and demonstrate cost improvements by at least 50% in large-scale scenarios with up to a thousand agents, compared with the original MAPF-LNS and other state-of-the-art methods.

Recent advances in diffusion models hold significant potential in robotics, enabling the generation of diverse and smooth trajectories directly from raw representations of the environment. Despite this promise, applying diffusion models to motion planning remains challenging due to their difficulty in enforcing critical constraints, such as collision avoidance and kinematic feasibility. These limitations become even more pronounced in Multi-Robot Motion Planning (MRMP), where multiple robots must coordinate in shared spaces. To address these challenges, this work proposes **S**imultaneous **M**RMP **D**iffusion (SMD), a novel approach integrating constrained optimization into the diffusion sampling process to produce collision-free, kinematically feasible trajectories. Additionally, the paper introduces a comprehensive MRMP benchmark to evaluate trajectory planning algorithms across scenarios with varying robot densities, obstacle complexities, and motion constraints. Experimental results show SMD consistently outperforms classical and other learning-based motion planners, achieving higher success rates and efficiency in complex multi-robot environments. The code and implementation are available at https://github.com/RAISELab-atUVA/Diffusion-MRMP.

A modern smart factory runs a manufacturing procedure using a collection of programmable machines. Typically, materials are ferried between these machines using a team of mobile robots. To embed a manufacturing procedure in a smart factory, a factory operator must a) assign its processes to the smart factory's machines and b) determine how agents should carry materials between machines. A good embedding maximizes the smart factory's throughput; the rate at which it outputs products. Existing smart factory management systems solve the aforementioned problems sequentially, limiting the throughput that they can achieve. In this paper we introduce ACES, the Anytime Cyclic Embedding Solver, the first solver which jointly optimizes the assignment of processes to machines and the assignment of paths to agents. We evaluate ACES and show that it can scale to real industrial scenarios.

Modern automated factories increasingly run manufacturing procedures using a matrix of programmable machines, such as 3D printers, interconnected by a programmable transport system, such as a fleet of tabletop robots. To embed a manufacturing procedure into a smart factory, an operator must: (a) assign each of its processes to a machine and (b) specify how agents should transport parts between machines. The problem of embedding a manufacturing process into a smart factory is termed the Smart Factory Embedding (SFE) problem. State-of-the-art SFE solvers can only scale to factories containing a couple dozen machines. Modern smart factories, however, may contain hundreds of machines. We fill this hole by introducing the first highly scalable solution to the SFE, TSACES, the Traffic System based Anytime Cyclic Embedding Solver. We show that TS-ACES is complete and can scale to SFE instances based on real industrial scenarios with more than a hundred machines.

Multi-Agent Path Finding (MAPF), which focuses on finding collision-free paths for multiple robots, is crucial for applications ranging from aerial swarms to warehouse automation. Solving MAPF is NP-hard so learning-based approaches for MAPF have gained attention, particularly those leveraging deep neural networks. Nonetheless, despite the community’s continued efforts, all learning-based MAPF planners still rely on decentralized planning due to variability in the number of agents and map sizes. We have developed the first centralized learning-based policy for MAPF problem called RAILGUN. RAILGUN is not an agent-based policy but a map-based policy. By leveraging a CNN-based architecture, RAILGUN can generalize across different maps and handle any number of agents. We collect trajectories from rule-based methods to train our model in a supervised way. In experiments, RAILGUN outperforms most baseline methods and demonstrates great zero-shot generalization capabilities on various tasks, maps and agent numbers that were not seen in the training dataset.

Multi-Agent Path Finding (MAPF) involves finding collision-free paths for multiple agents while minimizing a cost function—an NP-hard problem. Bounded suboptimal methods like Enhanced Conflict-Based Search (ECBS) and Explicit Estimation CBS (EECBS) balance solution quality with computational efficiency using focal search mechanisms. While effective, traditional focal search faces a limitation: the lower bound (LB) value determining which nodes enter the FOCAL list often increases slowly in early search stages, resulting in a constrained search space that delays finding valid solutions. In this paper, we propose a novel bounded suboptimal algorithm, double-ECBS (DECBS), to address this issue by first determining the maximum LB value and then employing a best-first search guided by this LB to find a collision-free path. Experimental results demonstrate that DECBS outperforms ECBS in most test cases and is compatible with existing optimization techniques. DECBS can reduce nearly 30% high-level Constraint Tree (CT) nodes and 50% low-level focal search nodes. When agent density is high, DECBS achieves a 23.5% average runtime improvement over ECBS with identical suboptimality bounds and optimizations.

Multi-Agent Path Finding (MAPF) is the problem of finding a set of collision-free paths, one for each agent in a shared environment. Its objective is to minimize the sum of path costs (SOC), where the path cost of each agent is defined as the travel time from its start location to its target location. Explicit Estimation Conflict-Based Search (EECBS) is the leading algorithm for bounded-suboptimal MAPF, with the SOC of the solution being at most a user-specified factor w away from optimal. EECBS maintains sets of paths and a lower bound LB on the optimal SOC. Then, it iteratively selects a set of paths whose SOC is at most w times LB and introduces constraints to resolve collisions. For each path in a set, EECBS maintains a lower bound on its optimal path that satisfies constraints. By finding a path with cost at most its threshold, defined as w times its lower bound, EECBS guarantees to find a bounded-suboptimal solution. To speed up EECBS, previous work uses flex distribution to relax the requirement that each path needs to be at most its threshold. Though EECBS with flex distribution guarantees to find a bounded-suboptimal solution, increasing the thresholds may increase the SOC beyond w times LB, forcing EECBS to switch among different sets of paths (whose SOC are still at most w times LB), and thus reducing efficiency. To address this issue, we propose Conflict-Based Flex Distribution that distributes flex in proportion to the number of collisions. We also estimate the extra travel time (i.e., delays) needed to satisfy constraints and propose Delay-Based Flex Distribution. On top of that, we propose Mixed-Strategy Flex Distribution, combining both in a hierarchical framework. We prove that EECBS with our new flex distribution mechanisms is complete and bounded-suboptimal. The experiments show that our approaches outperform the original (greedy) flex distribution. Also, we redesign Focal-A* search from the previous work to improve LB for a congested environment.

The bi-objective shortest-path (BOSP) problem seeks to find paths between start and target vertices of a graph while optimizing two conflicting objective functions. We consider the BOSP problem in the presence of correlated objectives. Such correlations often occur in real-world settings such as road networks, where optimizing two positively correlated objectives, such as travel time and fuel consumption, is common. BOSP is generally computationally challenging as the size of the search space is exponential in the number of objective functions and the graph size. Bounded sub-optimal BOSP solvers such as A*pex alleviate this complexity by approximating the Pareto-optimal solution set rather than computing it exactly (given a user-provided approximation factor). As the correlation between objective functions increases, smaller approximation factors are sufficient for collapsing the entire Pareto-optimal set into a single solution. We leverage this insight to propose an efficient algorithm that reduces the search effort in the presence of correlated objectives. Our approach for computing approximations of the entire Pareto-optimal set is inspired by graph-clustering algorithms. It uses a preprocessing phase to identify correlated clusters within a graph and to generate a new graph representation. This allows a natural generalization of A*pex to run up to five times faster on DIMACS dataset instances, a standard benchmark in the field. To the best of our knowledge, this is the first algorithm proposed that efficiently and effectively exploits correlations in the context of bi-objective search while providing theoretical guarantees on solution quality.

CBS is a state-of-the-art MAPF algorithm whose performance has been enhanced over the years by the introduction of heuristics that focus the search and reasoning techniques that identify specific types of conflicts that can be resolved faster. To further improve the efficiency of CBS, we present a novel idea based on constraint-reasoning techniques that merges similar high-level nodes close to the root of the constraint tree while preserving CBS' optimality. As a result, some of CBS' duplicate work that occurs when expanding similar high-level nodes is avoided. Our first experimental results using a simple CBS variant (ICBS-h) show a significant reduction in the number of expanded high-level nodes on average.

Multi-Agent Path Finding (MAPF), which focuses on finding collision-free paths for multiple robots, is crucial for applications ranging from aerial swarms to warehouse automation. Solving MAPF is NP-hard so learning-based approaches for MAPF have gained attention, particularly those leveraging deep neural networks. Nonetheless, despite the community's continued efforts, all learning-based MAPF planners still rely on decentralized planning due to variability in the number of agents and map sizes. We have developed the first centralized learning-based policy for MAPF problem called RAILGUN. RAILGUN is not an agent-based policy but a map-based policy. By leveraging a CNN-based architecture, RAILGUN can generalize across different maps and handle any number of agents. We collect trajectories from rule-based methods to train our model in a supervised way. In experiments, RAILGUN outperforms most baseline methods and demonstrates great zero-shot generalization capabilities on various tasks, maps and agent numbers that were not seen in the training dataset.

Multi-Agent Path Finding (MAPF) is the challenging problem of finding collision-free paths for multiple agents, which has a wide range of applications, such as automated warehouses, smart manufacturing, and traffic management. Recently, machine learning-based approaches have become popular in addressing MAPF problems in a decentralized and potentially generalizing way. Most learning-based MAPF approaches use reinforcement and imitation learning to train agent policies for decentralized execution under partial observability. However, current state-of-the-art approaches suffer from a prevalent bias to micro-aspects of particular MAPF problems, such as congestions in corridors and potential delays caused by single agents, leading to tight specializations through extensive engineering via oversized models, reward shaping, path finding algorithms, and communication. These specializations are generally detrimental to the sample efficiency, i.e., the learning progress given a certain amount of experience, and generalization to previously unseen scenarios. In contrast, curriculum learning offers an elegant and much simpler way of training agent policies in a step-by-step manner to master all aspects implicitly without extensive engineering. In this paper, we propose a generative curriculum approach to learning-based MAPF using Variational Autoencoder Utilized Learning of Terrains (VAULT). We introduce a two-stage framework to (I) train the VAULT via unsupervised learning to obtain a latent space representation of maps and (II) use the VAULT to generate curricula in order to improve sample efficiency and generalization of learning-based MAPF methods. For the second stage, we propose a bi-level curriculum scheme by combining our VAULT curriculum with a low-level curriculum method to improve sample efficiency further. Our framework is designed in a modular and general way, where each proposed component serves its purpose in a black-box manner without considering specific micro-aspects of the underlying problem. We empirically evaluate our approach in maps of the public MAPF benchmark set as well as novel artificial maps generated with the VAULT. Our results demonstrate the effectiveness of the VAULT as a map generator and our VAULT curriculum in improving sample efficiency and generalization of learning-based MAPF methods compared to alternative approaches. We also demonstrate how data pruning can further reduce the dependence on available maps without affecting the generalization potential of our approach.

Anytime multi-agent path finding (MAPF) is a promising approach to scalable path optimization in large-scale multi-agent systems. State-of-the-art anytime MAPF is based on Large Neighborhood Search (LNS), where a fast initial solution is iteratively optimized by destroying and repairing a fixed number of parts, i.e., the neighborhood of the solution, using randomized destroy heuristics and prioritized planning. Despite their recent success in various MAPF instances, current LNS-based approaches lack exploration and flexibility due to greedy optimization with a fixed neighborhood size which can lead to low-quality solutions in general. So far, these limitations have been addressed with extensive prior effort in tuning or offline machine learning beyond actual planning. In this paper, we focus on online learning in LNS and propose Bandit-based Adaptive LArge Neighborhood search Combined with Exploration (BALANCE). BALANCE uses a bi-level multi-armed bandit scheme to adapt the selection of destroy heuristics and neighborhood sizes on the fly during search. We evaluate BALANCE on multiple maps from the MAPF benchmark set and empirically demonstrate performance improvements of at least 50% compared to state-of-the-art anytime MAPF in large-scale scenarios. We find that Thompson Sampling performs particularly well compared to alternative multi-armed bandit algorithms.

In the Weight-Constrained Shortest-Path (WCSP) problem, given a graph in which each edge is annotated with a cost and a weight, a start state, and a goal state, the task is to compute a minimum-cost path from the start state to the goal state with weight no larger than a given weight limit. While most existing works have focused on solving the WCSP problem optimally, many real-world situations admit a trade-off between efficiency and a suboptimality bound for the path cost. In this paper, we propose the bounded-suboptimal WCSP algorithm WC-A*pex, which is built on the state-of-the-art approximate bi-objective search algorithm A*pex. WC-A*pex uses an approximate representation of paths with similar costs and weights to compute a (1+ε)-suboptimal path, for a given ε. During its search, WC-A*pex avoids storing all paths explicitly and thereby reduces the search effort while still retaining its (1 + ε)-suboptimality bound. On benchmark road networks, our experimental results show that WC-A*pex with ε = 0.01 (i.e., with a guaranteed suboptimality of at most 1%) achieves a speed-up of up to an order of magnitude over WC-A*, a state-of-the-art WCSP algorithm, and its bounded-suboptimal variant.

We present an empirical study of the relationship between map connectivity and the empirical hardness of the multi-agent pathfinding (MAPF) problem. By analyzing the second smallest eigenvalue (commonly known as lambda2) of the normalized Laplacian matrix of different maps, our initial study indicates that maps with smaller lambda2 tend to create more challenging instances when agents are generated uniformly randomly. Additionally, we introduce a map generator based on Quality Diversity (QD) that is capable of producing maps with specified lambda2 ranges, offering a possible way for generating challenging MAPF instances. Despite the absence of a strict monotonic correlation with lambda2 and the empirical hardness of MAPF, this study serves as a valuable initial investigation for gaining a deeper understanding of what makes a MAPF instance hard to solve.

The Multi-Objective Multi-Agent Path Finding (MO-MAPF) problem is the problem of computing collision-free paths for a team of agents while minimizing multiple cost metrics. Most existing MO-MAPF algorithms aim to compute the Pareto frontier. However, the Pareto frontier can be time-consuming to compute. Our first main contribution is BB-MO-CBS-pex, an approximate MO-MAPF algorithm that computes an approximate frontier for a user-specific approximation factor. BB-MO-CBS-pex builds upon BB-MO-CBS, a state-of-the-art MO-MAPF algorithm, and leverages A*pex, a state-of-the-art single-agent multi-objective search algorithm, to speed up different parts of BB-MO-CBS. We also provide two speed-up techniques for BB-MO-CBS-pex. Our second main contribution is BB-MO-CBS-k, which builds upon BB-MO-CBS-pex and computes up to k solutions for a user-provided k-value. BB-MO-CBS-k is useful when it is unclear how to determine an appropriate approximation factor. Our experimental results show that both BB-MO-CBS-pex and BB-MO-CBS-k solved significantly more instances than BB-MO-CBS for different approximation factors and k-values, respectively. Additionally, we compare BB-MO-CBS-pex with an approximate baseline algorithm derived from BB-MO-CBS and show that BB-MO-CBS-pex achieved speed-ups up to two orders of magnitude.

Coordinating a fleet of robots in unstructured, human-shared environments is challenging. Human behavior is hard to predict, and its uncertainty impacts the performance of the robotic fleet. Various multi-robot planning and coordination algorithms have been proposed, including Multi-Agent Path Finding (MAPF) methods to precedence-based algorithms. However, it is still unclear how human presence impacts different coordination strategies in both simulated environments and the real world. With the goal of studying and further improving multi-robot planning capabilities in those settings, we propose a method to develop and benchmark different multi-robot coordination algorithms in realistic, unstructured and human-shared environments. To this end, we introduce a multi-robot benchmark framework that is based on state-of-the-art open-source navigation and simulation frameworks and can use different types of robots, environments and human motion models. We show a possible application of the benchmark framework with two different environments and three centralized coordination methods (two MAPF algorithms and a loosely-coupled coordination method based on precedence constraints). We evaluate each environment for different human densities to investigate its impact on each coordination method. We also present preliminary results that show how informing each coordination method about human presence can help the coordination method to find faster paths for the robots.

We address the Virtual Network Embedding (VNE) problem in which the task is to map a virtual network onto a given physical substrate network so that the CPU and bandwidth capacity constraints are met. Following the success of Boolean Satisfiability (SAT) methods in areas such as Multi-Agent Path Finding (MAPF), we propose in this paper a novel SAT-based approach for solving the VNE problem. As in MAPF, the various constraints that define the VNE problem are encoded into the SAT models incrementally and via lazy refinements so as to keep the models simple. We also propose various model relaxations and concomitant solution extraction post-processing procedures. Through experiments, we show that our SAT-based approach outperforms other state-of-the-art approaches on a number of VNE instances.

In multi-objective search, given a directed graph where each edge is annotated with multiple cost metrics, a start state, and a goal state. We are interested in computing the Pareto frontier, i.e., the set of all undominated paths from the start state to the goal state. Almost all multi-objective search algorithms use dominance checks to determine if a search node can be pruned. Since dominance checks are performed in the inner loop of the multi-objective search, they are the most time-consuming part of it. In this paper, we propose (1) two novel techniques to reduce duplicate dominance checks and (2) a simple data structure that enables more efficient dominance checks. Our experimental results show that combining our proposed techniques and data structure speeds up LTMOA*, a state-of-the-art multi-objective search algorithm, by up to an order of magnitude on road network instances.

In the multi-objective search problem, a typical task is to compute the Pareto frontier, i.e., the set of all undominated solutions. However, computing the entire Pareto frontier can be very time-consuming, and in practice, we often have limited deliberation time. Therefore, this paper focuses on solving the multi-objective search problem with anytime algorithms, which compute an initial approximate frontier quickly and then work to find more solutions until eventually finding the entire Pareto frontier. Existing work has investigated such anytime algorithms for problem instances with only two objectives. In this paper, we propose Anytime A*pex (A-A*pex), which works with any number of objectives. In each iteration of A-A*pex, it runs A*pex, a state-of-the-art approximate multi-objective search algorithm, to compute more solutions. From one iteration to the next, A-A*pex can either reuse its previous search effort or restart from scratch. Our experimental results show that an A-A*pex variant that mixes reusing its search effort and restarting from scratch yields the best runtime performance. We also show that A-A*pex often computes solutions that collectively approximate the Pareto frontier much better than the solutions found by state-of-the-art multi-objective search algorithms for short deliberation times.

Facility Location Problems (FLPs) arise while serving multiple customers in a shared environment, minimizing transportation and other costs. Hence, they involve the optimal placement of facilities. They are defined on graphs as well as in Euclidean spaces with or without obstacles; and they are typically NP-hard to solve optimally. There are many heuristic algorithms tailored to different kinds of FLPs. However, FLPs defined in Euclidean spaces without obstacles are the most amenable to efficient and effective heuristic algorithms. This motivates the idea of quickly reformulating FLPs on graphs and in Euclidean spaces with obstacles to FLPs in Euclidean spaces without obstacles. Towards this end, we propose a new approach that uses FastMap and Locality Sensitive Hashing. FastMap is a near-linear-time algorithm that embeds the vertices of a graph in a Euclidean space while approximately preserving graph-based distances as Euclidean distances for all pairs of vertices. Through extensive experiments, we show that our approach significantly outperforms other state-of-the-art competing algorithms on a variety of FLPs: the Multi-Agent Meeting, Vertex K-Median (VKM), Weighted VKM, and the Capacitated VKM problems.

Research on multi-agent pathfinding (MAPF) has recently shifted towards problem variants that are closer to actual applications. Such variants often include the assignment of multiple goals to agents. To solve them, researchers have extended the Conflict Based Search (CBS) algorithm to multiple goals. This extension might look straightforward at first sight but it is tricky and this has already led to the development of algorithms that despite claiming to be optimal, return suboptimal solutions for some MAPF instances. In this paper, we provide a detailed analysis of the issue to raise awareness among the search community so that this mistake will not be perpetuated. Furthermore, a first evaluation against an optimal implementation is conducted which shows why this issue might have been difficult to spot. In only one of the randomly generated instances, the suboptimal behavior emerged.

Multi-Agent Path Finding (MAPF), i.e., finding collision-free paths for multiple robots, plays a critical role in many applications. Sometimes, assigning a target to each agent also presents a challenge. The Combined Target-Assignment and Path-Finding (TAPF) problem, a variant of MAPF, requires one to simultaneously assign targets to agents and plan collision-free paths for agents. Several algorithms, including CBM, CBS-TA, and ITA-CBS, optimally solve the TAPF problem, with ITA-CBS being the leading algorithm for minimizing flowtime. However, the only existing bounded-suboptimal algorithm ECBS-TA is derived from CBS-TA rather than ITA-CBS. So, it faces the same issues as CBS-TA, such as searching through multiple constraint trees and spending too much time on finding the next-best target assignment. We introduce ITA-ECBS, the first bounded-suboptimal variant of ITA-CBS. Transforming ITA-CBS to its bounded-suboptimal variant is challenging because different constraint tree nodes can have different assignments of targets to agents. ITA-ECBS uses focal search to achieve efficiency and determines target assignments based on a new lower bound matrix. We show that it runs faster than ECBS-TA in 87.42% of 54,033 test cases.

In the multi-objective shortest-path problem (MOSP) we are interested in finding paths between two vertices of a graph while considering multiple objectives. A key procedure, which dominates the running time of many state-of-the-art (SOTA) algorithms for MOSP is set dominance checks (SDC). In SDC, we are given a set X of N-dimensional tuples and a new N-dimensional tuple p and we need to determine whether there exists a tuple q in X such that q dominates p (i.e., if every element in q is lower or equal than the corresponding element in p). In this work, we offer a simple-yet-effective approach to perform SDC in a parallel manner, an approach that can be seamlessly integrated with most SOTA MOSP algorithms. Specifically, by storing states in memory dimension-wise and not state-wise, we can exploit vectorized operations offered by ``Single Instruction/Multiple Data'' (SIMD) instructions to efficiently perform SDC on ubiquitous consumer CPUs. Integrating our approach for SDC allows to dramatically improve the runtime of existing MOSP algorithms.

The development of connected and autonomous vehicles opens an opportunity to manage intersections without signals. One promising approach is to use a central autonomous intersection manager to optimize the movement of the vehicles in the intersection. Existing work uses Mixed Integer Linear Programming (MILP) to find optimal solutions for this problem but is time-consuming and cannot be applied in real-time. On the other hand, the coordination of the vehicles is essentially a Multi-Agent Path Finding (MAPF) problem, for which dozens of efficient algorithms have been proposed in recent years. Inspired by these MAPF algorithms, we propose a three-level algorithm called PSL to solve the intersection coordination problem. Theoretically, PSL is complete and polynomial-time in the number of vehicles. Empirically, PSL runs significantly faster with only a slight compromise in the solution quality than the optimal MILP method. It also generates significantly better solutions with a slightly larger runtime than the traditional First-Come-First-Served strategy.

We address the warehouse servicing problem (WSP) in automated warehouses, which use teams of mobile agents to bring products from shelves to packing stations. Given a list of products, the WSP amounts to finding a plan for a team of agents which brings every product on the list to a station within a given timeframe. The WSP consists of four subproblems, concerning what tasks to perform (task formulation), who will perform them (task allocation), and when (scheduling) and how (path planning) to perform them. These subproblems are NP-hard individually and are made more challenging by their interdependence. The difficulty of the WSP is compounded by the scale of automated warehouses, which frequently use teams of hundreds of agents. In this paper, we present a methodology that can solve the WSP at such scales. We introduce a novel, contract-based design framework which decomposes an automated warehouse into traffic system components. By assigning each of these components a contract describing the traffic flows it can support, we can syn-thesize a traffic flow satisfying a given WSP instance. Component-wise search-based path planning is then used to transform this traffic flow into a plan for discrete agents in a modular way. Evaluation shows that this methodology can solve WSP instances on real automated warehouses.

Virtualization is the mechanism of creating virtual representations of physical resources. It is now integrated into almost every facet of computing and is pervasive on the Internet: ranging from data center services and cloud computing services to services on our phones. The common goal for virtualization providers is to ensure that the physical resources are managed efficiently and effectively. This goal induces the Virtual Network Embedding (VNE) problem: the task of properly allocating the physical resources of a network to satisfy virtual requests for resources under various constraints while ensuring the quality of service and maximizing resource utilization. The VNE problem captures many resource allocation tasks arising in computer systems and computer networks. In this paper, we present Improved VNE-CBS (iVNE-CBS) as an efficient and effective algorithm for solving the VNE problem. iVNE-CBS builds on Conflict-Based Search (CBS), a heuristic search framework borrowed from the Multi-Agent Path Finding literature. We show that iVNECBS significantly outperforms popular baseline VNE algorithms: it scales to networks with several hundreds of vertices and thousands of edges, while also producing better-quality solutions.

Several successful approaches exist for solving the complex problem of multi-robot planning and coordination. Due to the lack of adequate benchmarking tools, comparing these approaches and judging their suitability for use in realistic scenarios is currently difficult. Therefore, we propose an open-source benchmark suite that aims to close this gap. Unlike existing benchmarks, our approach uses full-stack multi-robot navigation systems in realistic 3D simulated environments from the intralogistic and household domains. Using the open-source frameworks ROS 2, Gazebo and RMF allows the user to add other robot platforms easily. The framework provides easy-to-use abstractions, typical metrics and interfaces to several established planning libraries for multi-robot systems. With all these features, our framework successfully aids practitioners and researchers in comparing multi-robot planning and coordination systems to the state of the art. Our experiments show how the proposed benchmark simplifies gaining insights on relevant close to real-life robotics use cases.

In the multi-objective shortest-path problem we are interested in computing a path, or a set of paths that simultaneously balance multiple cost functions. This problem is important for a diverse range of applications such as transporting hazardous materials considering travel distance and risk. This family of problems is not new with results dating back to the 1970's. Nevertheless, the significant progress made in the field of heuristic search resulted in a new and growing interest in the sub-field of multi-objective search. Consequently, in this paper we review the fundamental problems and techniques common to most algorithms and provide a general overview of the field. We then continue to describe recent work with an emphasis on new challenges that emerged and the resulting research opportunities.

We address the Warehouse Servicing Problem (WSP) in automated warehouses, which use teams of mobile robots to move products from shelves to packaging stations. Given a list of products, the WSP amounts to finding a motion plan which brings every product on the list from a shelf to a packaging station within a given time limit. The WSP consists of four subproblems, namely, deciding where to source and deposit a product (task formulation), who should transport each product (task assignment) and when (scheduling) and how (motion planning). These problems are NP-Hard individually and made more challenging by their interdependence. The difficulty of the WSP is compounded by the scale of automated warehouses, which use teams of hundreds of agents to transport thousands of products. In this paper, we present Contract-based Cyclic Motion Planning (CCMP), a novel contract-based methodology for solving the WSP at scale. CCMP decomposes a warehouse into a set of traffic system components. By assigning each component a contract which describes the traffic flows it can support, CCMP can generate a traffic flow which satisfies a given WSP instance. CCMP then uses a novel motion planner to transform this traffic flow into a motion plan for a team of robots. Evaluation shows that CCMP can solve WSP instances taken from real industrial scenarios with up to 1 million products while outperforming other methodologies for solving the WSP by up to 2.9×.

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths, one for each agent, in a shared environment, while minimizing their sum of travel times. Since solving MAPF optimally is NP-hard, researchers have explored algorithms that solve MAPF suboptimally but efficiently. Priority-Based Search (PBS) is the leading algorithm for this purpose. It finds paths for individual agents, one at a time, and resolves collisions by assigning priorities to the colliding agents and replanning their paths during its search. However, PBS becomes ineffective for MAPF instances with high densities of agents and obstacles. Therefore, we introduce Greedy PBS (GPBS), which uses greedy strategies to speed up PBS by minimizing the number of collisions between agents. We then propose techniques that speed up GPBS further, namely partial expansions, target reasoning, induced constraints, and soft restarts. We show that GPBS with all these improvements has a higher success rate than the state-of-the-art suboptimal algorithm for a 1-minute runtime limit, especially for MAPF instances with small maps and dense obstacles.

This extended abstract presents a theoretical analysis of node expansions in Multi-Objective Search. We define three categories of nodes, Must-Expand Nodes, Maybe-Expand Nodes, and Never-Expand Nodes. Our analysis establishes that regardless of the Ordering Function or Multi-Objective Search algorithm used, any Multi-Objective Search algorithm must expand all Must-Expand Nodes, some or none of Maybe-Expand Nodes, and none of Never-Expand Nodes. In addition, we conduct experimental evaluations of various Ordering Functions, revealing that they all expand the same number of nodes and compare their efficiency at finding solutions at various stages of the search.

In bi-objective graph search, each edge is annotated with a cost pair, where each cost corresponds to an objective to optimize. We are interested in finding all undominated paths from a given start state to a given goal state (called the Pareto front). Almost all existing works of bi-objective search use single-valued heuristics, which use one number for each objective, to estimate the cost between any given state and the goal state. However, single-valued heuristics cannot reflect the trade-offs between the two costs. On the other hand, multi-valued heuristics use a set of pairs to estimate the Pareto front between any given state and the goal state and are more informed than single-valued heuristics. However, they are rarely studied and have yet to be investigated in explicit state spaces by any existing work. In this paper, we are interested in using multi-valued heuristics to improve bi-objective search algorithms in explicit state spaces. More specifically, we generalize Differential Heuristics (DHs), a class of memory-based heuristics for single-objective search, to bi-objective search, resulting in Bi-objective Differential Heuristics (BO-DHs). We propose several techniques to reduce the memory usage and computational overhead of BO-DHs significantly. Our experimental results show that, with suggested improvement and tuned parameters, BO-DHs can reduce the node expansion and runtime of a bi-objective search algorithm by up to an order of magnitude, paving the way for more effective multi-valued heuristics.

Multi-Agent Path Finding (MAPF) is the problem of planning collision-free paths for multiple agents in a shared environment. In this paper, we propose a novel algorithm MAPF-LNS2 based on large neighborhood search for solving MAPF efficiently. Starting from a set of paths that contain collisions, MAPF-LNS2 repeatedly selects a subset of colliding agents and replans their paths to reduce the number of collisions until the paths become collision-free. We compare MAPF-LNS2 against a variety of state-of-the-art MAPF algorithms, including Prioritized Planning with random restarts, EECBS, and PPS, and show that MAPF-LNS2 runs significantly faster than them while still providing near-optimal solutions in most cases. MAPF-LNS2 solves 80% of the random-scenario instances with the largest number of agents from the MAPF benchmark suite with a runtime limit of just 5 minutes, which, to our knowledge, has not been achieved by any existing algorithms.

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents that minimize the sum of path costs. EECBS is a leading two-level algorithm that solves MAPF bounded-suboptimally, that is, within some factor w of the minimum sum of path costs C*. It uses focal search to find bounded-suboptimal paths on the low level and Explicit Estimation Search (EES) to resolve collisions on the high level. EES keeps track of a lower bound LB on C* to find paths whose sum of path costs is at most w LB in order to solve MAPF bounded-suboptimally. However, the costs of many paths are often much smaller than w times their minimum path costs, meaning that the sum of path costs is much smaller than w C*. In this paper, we therefore propose Flexible EECBS (FEECBS), which uses a flex(ible) distribution of the path costs (that relaxes the requirement to find bounded-suboptimal paths on the low level) in order to reduce the number of collisions that need to be resolved on the high level while still guaranteeing to solve MAPF bounded suboptimally. We address the drawbacks of flex distribution via techniques such as restrictions on the flex distribution, restarts of the high-level search with EECBS, and low-level focal-A* search. Our empirical evaluation shows that FEECBS substantially improves the efficiency of EECBS on MAPF instances with large maps and large numbers of agents.

Multi-Agent Path Finding (MAPF) is the problem of finding a set of collision-free paths for a team of agents in a common environment. MAPF is NP-hard to solve optimally and, in some cases, also bounded-suboptimally. It is thus time-consuming for (bounded-sub)optimal solvers to solve large MAPF instances. Anytime algorithms find solutions quickly for large instances and then improve them to close-to-optimal ones over time. In this paper, we improve the current state-of-the-art anytime solver MAPF-LNS, that first finds an initial solution fast and then repeatedly replans the paths of subsets of agents via Large Neighborhood Search (LNS). It generates the subsets of agents for replanning by randomized destroy heuristics, but not all of them increase the solution quality substantially. We propose to use machine learning to learn how to select a subset of agents from a collection of subsets, such that replanning increases the solution quality more. We show experimentally that our solver, MAPF-ML-LNS, significantly outperforms MAPF-LNS on the standard MAPF benchmark set in terms of both the speed of improving the solution and the final solution quality.

Modern multi-agent robotic systems increasingly require scalable, robust and persistent Multi-Agent Path Finding (MAPF) with performance guarantees. While many MAPF solvers that provide some of these properties exist, none provides them all. To fill this need, we propose a new MAPF framework, the shard system. A shard system partitions the workspace into geographic regions, called shards, linked by a novel system of buffers. Agents are routed optimally within a shard by a local controller to local goals set by a global controller. The buffer system novelly allows shards to plan with perfect parallelism, providing scalability. A novel global controller algorithm can rapidly generate an inter-shard routing plan for thousands of agents while minimizing the traffic routed through any shard. A novel workspace partitioning algorithm produces shards small enough to replan rapidly. These innovations allow a shard system to adjust its routing plan in real time if an agent is delayed or assigned a new goal, enabling robust, persistent MAPF. A shard system's local optimality and optimized inter-shard routing bring the sum-of-costs of its solutions to single-shot MAPF problems to < 20-60% of optimal on a diversity of workspaces. Its scalability allows it to plan paths for 1000s of agents in seconds. If any of their goals change or move actions fails, a shard system can replan in under a second.

(Dis)Appearables is an approach for actuated Tangible User Interfaces (TUIs) to appear and disappear. This technique is supported by Stages: physical platforms inspired by theatrical stages. Self-propelled TUI’s autonomously move between front and back stage allowing them to dynamically appear and disappear from users’ attention. This platform opens up a novel interaction design space for expressive displays with dynamic physical affordances.

We formalize and study the multi-goal task assignment and path finding (MG-TAPF) problem from theoretical and algorithmic perspectives. The MG-TAPF problem is to compute an assignment of tasks to agents, where each task consists of a sequence of goal locations, and collision-free paths for the agents that visit all goal locations of their assigned tasks in sequence. Theoretically, we prove that the MG-TAPF problem is NP-hard to solve optimally. We present algorithms that build upon algorithmic techniques for the multi-agent path finding problem and solve the MG-TAPF problem optimally and bounded-suboptimally. We experimentally compare these algorithms on a variety of different benchmark domains.

In this work, we consider the Multi-Agent Pickup-and-Delivery (MAPD) problem, where agents constantly engage with new tasks and need to plan collision-free paths to execute them. To execute a task, an agent needs to visit a pair of goal locations, consisting of a pickup location and a delivery location. We propose two variants of an algorithm that assigns a sequence of tasks to each agent using the anytime algorithm Large Neighborhood Search (LNS) and plans paths using the Multi-Agent Path Finding (MAPF) algorithm Priority-Based Search (PBS). LNS-PBS is complete for well-formed MAPD instances, a realistic subclass of MAPD instances, and empirically more effective than the existing complete MAPD algorithm CENTRAL. LNS-wPBS provides no completeness guarantee but is empirically more efficient and stable than LNS-PBS. It scales to thousands of agents and thousands of tasks in a large warehouse and is empirically more effective than the existing scalable MAPD algorithm HBH+MLA*. LNS-PBS and LNS-wPBS also apply to a more general variant of MAPD, namely the Multi-Goal MAPD (MG-MAPD) problem, where tasks can have different numbers of goal locations.

In Multi-Agent Pathfinding (MAPF), the task is to find non-colliding paths for a set of agents. This paper focuses on search-based MAPF algorithms from the Conflict-Based Framework, which is introduced here. A common technique in such algorithms is to merge a group of dependent agents into a meta-agent and plan non-colliding paths for the meta-agent using a low-level MAPF sub-solver. We analyze the patterns that emerge when agents are merged in an arbitrary order. We then introduce policies for choosing which agents or meta-agents to merge to achieve improved efficiency in three algorithms: Independence Detection (ID) and Improved Conflict-Based Search (ICBS), which are optimal, and Priority-Based Search (PBS), which is a fast suboptimal algorithm. Experimental results show a significant improvement in efficiency

Multi-Train Path Finding (MTPF) is a coordination problem that asks us to plan collision-free paths for a team of moving agents, where each agent occupies a sequence of locations at any given time. MTPF is useful for planning a range of real-world vehicles, including rail trains and road convoys. MTPF is closely related to another coordination problem known as k-Robust Multi-Agent Path Finding (kR-MAPF). Although similar in principle, the performance of optimal MTPF algorithms in practice lags far behind that of optimal kR-MAPF algorithms. In this work, we revisit the connection between them and reduce the performance gap. First, we show that, in many cases, a valid kR-MAPF plan is also a valid MTPF plan, which leads to a new and faster approach for collision resolution. We also show that many recently introduced improvements for kR-MAPF, such as lower-bounding heuristics and symmetry reasoning, can be extended to MTPF. Finally, we explore a new type of pairwise symmetry specific to MTPF. Our experiments show that these improvements yield large efficiency gains for optimal MTPF.

In this work, we examine a line of recent publications that propose to use deep neural networks to approximate the goal distances of states for heuristic search. We present a first step toward showing that this work suffers from inherent scalability limitations since --- under the assumption that P≠NP --- such approaches require network sizes that scale exponentially in the number of states to achieve the necessary (high) approximation accuracy.

There are many settings that extend the basic shortest path search problem. In Bounded-Cost Search, we are given a constant bound and the task is to find a solution within the bound. In Bi-Objective Search, each edge is associated with two costs (objectives) and the task is to minimize both objectives. In this paper, we combine both these settings into a new setting of Bounded-Cost Bi-Objective Search. We are given two bounds, one for each objective and the task is to find a solution within these bounds. We provide a scheme for normalizing the two objectives. We then introduce several algorithms for this new setting and compare them experimentally.

Multi-Agent Path Finding (MAPF) algorithms and their variants can find high-quality collision-free plans for automated warehousing under simplified assumptions about the robot dynamics. However, these simplifying assumptions pose challenging implementational issues as the robots cannot follow the plans precisely. Various robust execution frameworks, such as the Action Dependency Graph (ADG) framework, have been proposed to enable the real-world execution of MAPF plans. Under such a framework, it is unclear how the simplifying assumptions affect the performance of the robots. In this work, we first argue that the ADG framework provides the same robustness guarantees as the single-agent framework (where plans are generated independently for each robot and collisions are avoided through a reservation table), which is widely used in industry. We then improve the efficiency of the ADG framework by integrating it with the Rolling-Horizon Collision-Resolution framework to solve MAPF problems with a persistent stream of online tasks. Using the integrated framework, we compare the standard MAPF model with many of its more complex variants, such as MAPF with rotation, k-robust MAPF, and continuous-time MAPF (taking robot dynamics into account). We examine their effectiveness in improving throughput through realistic simulations of warehouse settings with the Gazebo simulator.

Prioritized Planning (PP) is a fast and popular framework for solving Multi-Agent Path Finding, but its solution quality depends heavily on the predetermined priority ordering of the agents. Current PP algorithms use either greedy policies or random assignments to determine a total priority ordering, but none of them dominates the others in terms of the success rate and solution quality (measured by the sum-of-costs). We propose a machine-learning (ML) framework to learn a good priority ordering for PP. We develop two models, namely ML-T, which is trained on a total priority ordering, and ML-P, which is trained on a partial priority ordering. We propose to boost the effectiveness of PP by further applying stochastic ranking and random restarts. The results show that our ML-guided PP algorithms outperform the existing PP algorithms in success rate, runtime, and solution quality on small maps in most cases and are competitive with them on large maps despite the difficulty of collecting training data on these maps.

Mutex propagation and its concomitant symmetry-breaking techniques have proven useful in Multi-Agent Path Finding (MAPF) with point agents. In this paper, we show that they can be easily generalized to richer MAPF problems. In particular, we demonstrate their application to MAPF with ``Large'' Agents (LA-MAPF). Here, agents can occupy multiple points at the same time according to their fixed shapes and sizes. While existing rule-based symmetry-breaking techniques are difficult to generalize from point agents to large agents, mutex-based symmetry-breaking techniques can be generalized easily. In a Conflict-Based Search (CBS) framework for LA-MAPF, we also develop a mutex-based conflict-selection strategy to further enhance the efficiency of the search. Through experiments on various maps, we show that our techniques significantly improve MC-CBS, a state-of-the-art optimal LA-MAPF algorithm, in terms of both success rate and runtime.

The Pareto-optimal frontier for a bi-objective search problem instance consists of all solutions that are not worse than any other solution in both objectives. The size of the Pareto-optimal frontier can be exponential in the size of the input graph, and hence finding it can be hard. Some existing works leverage a user-specified approximation factor epsilon to compute an approximate Pareto-optimal frontier that can be significantly smaller than the Pareto-optimal frontier. In this paper, we propose an anytime approximate bi-objective search algorithm, called Anytime Bi-Objective A*-epsilon (A-BOA*). A-BOA* is useful when deliberation time is limited. It first finds an approximate Pareto-optimal frontier quickly, iteratively improves it while time allows, and eventually finds the Pareto-optimal frontier. It efficiently reuses the search effort from previous iterations and makes use of a novel pruning technique. Our experimental results show that A-BOA* substantially outperforms baseline algorithms that do not reuse previous search effort, both in terms of runtime and number of node expansions. In fact, the most advanced variant of A-BOA* even slightly outperforms BOA*, a state-of-the-art bi-objective search algorithm, for finding the Pareto-optimal frontier. Moreover, given only a limited amount of deliberation time, A-BOA* finds solutions that collectively approximate the Pareto-optimal frontier much better than the solutions found by BOA*.

Multi-Agent Path Finding (MAPF), i.e., finding collision-free paths for multiple robots, is important for many applications where small runtimes are necessary, including the kind of automated warehouses operated by Amazon. CBS is a leading two-level search algorithm for solving MAPF optimally. ECBS is a bounded-suboptimal variant of CBS that uses focal search to speed up CBS by sacrificing optimality and instead guaranteeing that the costs of its solutions are within a given factor of optimal. In this paper, we study how to decrease its runtime even further using inadmissible heuristics. Motivated by Explicit Estimation Search (EES), we propose Explicit Estimation CBS (EECBS), a new bounded-suboptimal variant of CBS, that uses online learning to obtain inadmissible estimates of the cost of the solution of each high-level node and uses EES to choose which high-level node to expand next. We also investigate recent improvements of CBS and adapt them to EECBS. We find that EECBS with the improvements runs significantly faster than the state-of-the-art bounded-suboptimal MAPF algorithms ECBS, BCP-7, and eMDD-SAT on a variety of MAPF instances. We hope that the scalability of EECBS enables additional applications for bounded-suboptimal MAPF algorithms.

Multi-Agent Path Finding (MAPF) is the problem of moving a team of agents to their goal locations without collisions. In this paper, we study the lifelong variant of MAPF, where agents are constantly engaged with new goal locations, such as in large-scale automated warehouses. We propose a new framework Rolling-Horizon Collision Resolution (RHCR) for solving lifelong MAPF by decomposing the problem into a sequence of Windowed MAPF instances, where a Windowed MAPF solver resolves collisions among the paths of the agents only within a bounded time horizon and ignores collisions beyond it. RHCR is particularly well suited to generating pliable plans that adapt to continually arriving new goal locations. We empirically evaluate RHCR with a variety of MAPF solvers and show that it can produce high-quality solutions for up to 1,000 agents (= 38.9% of the empty cells on the map) for simulated warehouse instances, significantly outperforming existing work.

Conflict-Based Search (CBS) is a leading two-level algorithm for optimal Multi-Agent Path Finding (MAPF). The main step of CBS is to expand nodes by resolving conflicts (where two agents collide). Choosing the ‘right’ conflict to resolve can greatly speed up the search. CBS first resolves conflicts where the costs (g-values) of the resulting child nodes are larger than the cost of the node to be split. However, the recent addition of high-level heuristics to CBS and expanding nodes according to f=g+h reduces the relevance of this conflict prioritization method. Therefore, we introduce an expanded categorization of conflicts, which first resolves conflicts where the f-values of the child nodes are larger than the f-value of the node to be split, and present a method for identifying such conflicts. We also enhance all known heuristics for CBS by using information about the cost of resolving certain conflicts, and with only a small computational overhead. Finally, we experimentally demonstrate that both the expanded categorization of conflicts and the improved heuristics contribute to making CBS even more efficient.

Conflict-Based Search (CBS) is a state-of-the-art algorithm for multi-agent path finding. On the high level, CBS repeatedly detects conflicts and resolves one of them by splitting the current problem into two subproblems. Previous work chooses the conflict to resolve by categorizing conflicts into three classes and always picking one from the highest-priority class. In this work, we propose an oracle for conflict selection that results in smaller search tree sizes than the one used in previous work. However, the computation of the oracle is slow. Thus, we propose a machine-learning (ML) framework for conflict selection that observes the decisions made by the oracle and learns a conflict-selection strategy represented by a linear ranking function that imitates the oracle's decisions accurately and quickly. Experiments on benchmark maps indicate that our approach, ML-guided CBS, significantly improves the success rates, search tree sizes and runtimes of the current state-of-the-art CBS solver.

Multi-Agent Path Finding (MAPF) is the challenging problem of computing collision-free paths for multiple agents. Algorithms for solving MAPF can be categorized on a spectrum. At one end are (bounded-sub)optimal algorithms that can find high-quality solutions for small problems. At the other end are unbounded-suboptimal algorithms that can solve large problems but usually find low-quality solutions. In this paper, we consider a third approach that combines the best of both worlds: anytime algorithms that quickly find an initial solution using efficient MAPF algorithms from the literature, even for large problems, and that subsequently improve the solution quality to near-optimal as time progresses by replanning subgroups of agents using Large Neighborhood Search. We compare our algorithm MAPF-LNS against a range of existing work and report significant gains in scalability, runtime to the initial solution, and speed of improving the solution.

Multi-Agent Path Finding (MAPF) is the combinatorial problem of finding collision-free paths for multiple agents on a graph. This paper describes MAPF-based software for solving train planning and replanning problems on large-scale railway networks under uncertainty. The software recently won the 2020 Flatland Challenge, a NeurIPS competition trying to determine how to efficiently manage dense traffic on rail networks. The software incorporates many state-of-the-art MAPF, or in general, optimization technologies, such as prioritized planning, large neighborhood search, safe interval path planning, minimum communication policies, parallel computing, and simulated annealing. It can plan collision-free paths for thousands of trains within a few minutes and deliver deadlock-free actions in real-time during execution.

Conflict-Based Search (CBS) is a leading two-level algorithm for optimal Multi-Agent Path Finding (MAPF). At its high level, CBS expands nodes by resolving conflicts. In recent years, admissible heuristics were added to the high level of CBS. We enhance all known heuristic functions for CBS by using information about the cost of resolving certain conflicts, with only a small computational overhead. We experimentally demonstrate that the improved heuristics contribute to making CBS even more efficient.

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents. CBS is a leading optimal two-level MAPF solver whose low level plans optimal paths for single agents and whose high level runs a best-first search on a Constraint Tree (CT) to resolve the collisions between the paths. ECBS, a bounded-suboptimal variant of CBS, speeds up CBS by reducing the number of collisions that need to be resolved on the high level. It achieves this by generating bounded-suboptimal paths with fewer collisions with the paths of the other agents on the low level and expanding bounded-suboptimal CT nodes that contain fewer collisions on the high level. In this paper, we propose Flexible ECBS (FECBS) that further reduces the number of collisions that need to be resolved on the high level by using looser suboptimal bounds on the low level while still providing bounded-suboptimal solutions. Instead of requiring the cost of each path to be bounded-suboptimal, FECBS requires only the overall cost of the paths to be bounded-suboptimal, which gives us the freedom to distribute the cost leeway among different agents according to their needs. Our empirical results show that FECBS can solve more MAPF instances than state-of-the-art ECBS variants within 5 minutes.

Solving Multi-Agent Path Finding (MAPF) instances optimally is NP-hard, and existing optimal and bounded suboptimal MAPF solvers thus usually do not scale to large MAPF instances. Greedy MAPF solvers scale to large MAPF instances, but their solution qualities are often bad. In this paper, we therefore propose a novel MAPF solver, Hierarchical Multi-Agent Path Planner (HMAPP), which creates a spatial hierarchy by partitioning the environment into multiple regions and decomposes a MAPF instance into smaller MAPF sub-instances for each region. For each sub-instance, it uses a bounded-suboptimal MAPF solver to solve it with good solution quality. Our experimental results show that HMAPP is able to solve as large MAPF instances as greedy MAPF solvers while achieving better solution qualities on various maps.

We report on an experiment that we performed when we taught the undergraduate artificial intelligence class at the University of Southern California. We taught it – under very similar conditions – once with and once without an attendance requirement. The attendance requirement substantially increased the attendance of the students. It did not substantially affect their performance but decreased their course ratings across all categories in the official course evaluation, whose results happened to be biased toward the opinions of the students attending the lectures. For example, the overall rating of the instructor was 0.89 lower (on a 1-5 scale) with the attendance requirement and the overall rating of the class was 0.85 lower. Thus, the attendance requirement, combined with the policy for administering the course evaluation, had a large impact on the course ratings, which is a problem if the course ratings influence decisions on promotions, tenure, and salary increments for the instructors but also demonstrates the potential for the manipulation of course ratings.

In this paper, we study the one-shot and lifelong versions of the Target Assignment and Path Finding problem in automated sortation centers, where each agent needs to constantly assign itself a sorting station, move to its assigned station without colliding with obstacles or other agents, wait in the queue of that station to obtain a parcel for delivery, and then deliver the parcel to a sorting bin. The throughput of such centers is largely determined by the total idle time of all stations since their queues can frequently become empty. To address this problem, we first formalize and study the one-shot version that assigns stations to a set of agents and finds collision-free paths for the agents to their assigned stations. We present efficient algorithms for this task based on a novel min-cost max-flow formulation that minimizes the total idle time of all stations in a fixed time window. We then demonstrate how our algorithms for solving the one-shot problem can be applied to solving the lifelong problem as well. Experimentally, we believe to be the first researchers to consider real-world automated sortation centers using an industrial simulator with realistic data and a kinodynamic model of real robots. On this simulator, we showcase the benefits of our algorithms by demonstrating their efficiency and effectiveness for up to 350 agents.

The Model AI Assignments session seeks to gather and disseminate the best assignment designs of the Artificial Intelligence (AI) Education community. Recognizing that assignments form the core of student learning experience, we here present abstracts of nine AI assignments from the 2020 session that are easily adoptable, playfully engaging, and flexible for a variety of instructor needs. Assignment specifications and supporting resources may be found at http://modelai.gettysburg.edu.

The weighted constraint satisfaction problem (WCSP) is a general and very useful combinatorial optimization tool. Despite its importance, the task of generating the top K solutions to it is understudied. One benefit of generating the top K solutions is in creating a framework for “human-in-the-loop AI”. Most real-world problems cannot be modeled accurately/completely up front and, hence, generating the top K solutions gives users a chance to exercise preferences that are not explicitly included in the modeling phase. In this paper, we first discuss the importance of generating the top K solutions to WCSPs in various contexts. We then propose various approaches to do so and empirically compare them. We include approaches based on quadratization, pseudo-Boolean optimization, constraint propagation, and integer linear programming. Together, they cover all major algorithmic ingredients derived from constraint programming (CP), artificial intelligence (AI), and operations research (OR).

In the Multi-Agent Meeting problem (MAM), the task is to find a meeting location for multiple agents, as well as a path for each agent to that location. In this paper, we introduce MM*, a Multi-Directional Heuristic Search algorithm that finds the optimal meeting location under different cost functions. MM* generalizes the Meet in the Middle (MM) bidirectional search algorithm to the case of finding an optimal meeting location for multiple agents. Several admissible heuristics are proposed, and experiments demonstrate the benefits of MM*.

Conflict-Based Search (CBS) is a leading algorithm for optimal Multi-Agent Path Finding (MAPF). CBS variants typically compute MAPF solutions using some form of A* search. However, they often do so under strict time limits so as to avoid exhausting the available memory. In this paper, we present IDCBS, an iterative-deepening variant of CBS which can be executed without exhausting the memory and without strict time limits. IDCBS can be substantially faster than CBS due to incremental methods that it uses when processing CBS nodes.

In this paper, we formalize and study the Moving Agents in Formation (MAiF) problem, that combines the tasks of finding short collision-free paths for multiple agents and keeping them in close adherence to a desired formation. Previous work includes controller-based algorithms, swarm-based algorithms, and potential-field-based algorithms. They usually focus on only one or the other of these tasks, solve the problem greedily without systematic search, and thus generate costly solutions or even fail to find solutions in congested environment. In this paper, we develop a two-phase search algorithm, called SWARM-MAPF, whose first phase is inspired by swarm-based algorithms (in open regions) and whose second phase is inspired by multi-agent path-finding (MAPF) algorithms (in congested regions). In the first phase, SWARM-MAPF selects a leader among the agents and finds a path for it that is sufficiently far away from the obstacles so that the other agents can preserve the desired formation around it. It also identifies the critical segments of the leader's path where the other agents cannot preserve the desired formation and the refinement of which has thus to be delegated to the second phase. In the second phase, SWARM-MAPF refines these segments. Theoretically, we prove that SWARM-MAPF is complete. Empirically, we show that SWARM-MAPF scales well and is able to find close-to-optimal solutions.

We consider two new types of pairwise path symmetries which appear in the context of Multi-Agent Path Finding (MAPF). The first of them, corridor symmetry, arises when two agents attempt to pass through the same narrow passage but in opposite directions. The second, target symmetry, arises when the shortest path of one agent requires the target location of a second agent after the second agent has already arrived. These symmetries can produce an exponential blowup in the space of possible collision resolutions, leading to timeout failure even for state-of-the-art algorithms such as Conflict-Based Search. We propose to break symmetries using new reasoning techniques that: (1) detect each type of situation and, (2) resolve them by introducing specialized constraints. We implement our ideas in the context of Conflict-Based Search where, in a range of experiments, we report up to an order-of-magnitude improvement in runtime performance and, in some cases, more than a doubling in success rate.

The weighted constraint satisfaction problem (WCSP) is a powerful mathematical framework for combinatorial optimization. The branch and bound search paradigm is very successful in solving the WCSP but critically depends on the ordering in which variables are instantiated. In this paper, we introduce a new framework for dynamic variable ordering for solving the WCSP. This framework is inspired by regression decision tree learning. Variables are ordered dynamically based on samples of random assignments of values to variables as well as their corresponding total weights. Within this framework, we propose four variable ordering heuristics (sdr, inv-sdr, rr and inv-rr). We compare them with many other state-of-the-art dynamic variable ordering heuristics, and show that sdr and rr outperform them on many real-world and random benchmark instances.

In the Multi-Agent Meeting (MAM) problem, the task is to find a meeting location for multiple agents, as well as a path for each agent to that location. In this paper, we introduce MM*, a Multi-Directional Search algorithm that finds the optimal meeting location under different cost functions. MM* generalizes the Meet in the Middle (MM) bidirectional search algorithm to the case of finding optimal meeting locations for multiple agents. A number of admissible heuristics are proposed and experiments demonstrate the benefits of MM*.

The 2D Multi-Agent Path Finding (MAPF) problem aims at finding collision-free paths for a number of agents, from a set of start locations to a set of goal positions in a known 2D environment. MAPF has been studied in theoretical computer science, robotics, and artificial intelligence over several decades, due to its importance for robot navigation. It is currently experiencing significant scientific progress due to its relevance in automated warehousing (such as those operated by Amazon) and in other contemporary application areas. In this paper, we demonstrate that some recently developed MAPF algorithms apply more broadly than currently believed in the MAPF research community. In particular, we describe the 3D Pipe Routing (PR) problem, which aims at placing collision-free pipes from given start locations to given goal locations in a known 3D environment. The MAPF and PR problems are similar: a solution to a MAPF instance is a set of blocked cells in x-y-t space, while a solution to the corresponding PR instance is a set of blocked cells in x-y-z space. We show how to use this similarity to apply several recently developed MAPF algorithms to the PR problem, and discuss their performance on real-world PR instances. This opens up a new direction of industrial relevance for the MAPF research community.

Embedding undirected graphs in a Euclidean space has many computational benefits. FastMap is an efficient embedding algorithm that facilitates a geometric interpretation of problems posed on undirected graphs. However, Euclidean distances are inherently symmetric and, thus, Euclidean embeddings cannot be used for directed graphs. In this paper, we present FastMap-D, an efficient generalization of FastMap to directed graphs. FastMap-D embeds vertices using a potential field to capture the asymmetry between the to-and-fro pairwise distances in directed graphs. FastMap-D learns a potential function to define the potential field using a machine learning module. In experiments on various kinds of directed graphs, we demonstrate the advantage of FastMap-D over other approaches.

Paths found on grid graphs are often unrealistic looking in the continuous environment that the grid graph represents and often need to be smoothed after a search. The well-known algorithm for path smoothing is greedy in nature and does not necessarily eliminate all heading changes in freespace. We present a new path-smoothing algorithm based on “string pulling” and show experimentally that it consistently finds shorter paths than the greedy algorithm and produces paths with no heading changes in freespace.

Many interesting search problems can be formulated as bi-objective search problems; for example, transportation problems where both travel distance and time need to be minimized. Multi-objective best-first search algorithms need to maintain the set of undominated paths from the start state to each state to compute a set of paths from a given start state to a given goal state (the Pareto-optimal solutions) such that no path in the set is dominated by another path in the set. Each time they find a new path to a state n, they perform a dominance check to determine whether such a path dominates any of the previously found paths to n. Existing algorithms do not perform these checks efficiently, requiring at least a full iteration over the Open list per check. In this paper, we present the first multi-objective algorithm that performs these checks efficiently. Indeed, Bi-Objective A* (BOA*)—our algorithm—requires constant time to check for dominance. Our experimental evaluation shows that BOA*is orders-of-magnitude faster than state-of-the-art search algorithms, such as NAMOA*, Bi-Objective Dijkstra, and Bidirectional Bi-Objective Dijkstra.

The Multi-Agent Pickup and Delivery (MAPD) problem models applications where a large number of agents attend to a stream of incoming pickup-and-delivery tasks. Token Passing (TP) is a recent MAPD algorithm that is efficient and effective. We make TP even more efficient and effective by using a novel combinatorial search algorithm, called Safe Interval Path Planning with Reservation Table (SIPPwRT), for single-agent path planning. SIPPwRT uses an advanced data structure that allows for fast updates and lookups of the current paths of all agents in an online setting. The resulting MAPD algorithm TP-SIPPwRT takes kinematic constraints of real robots into account directly during planning, computes continuous agent movements with given velocities that work on non-holonomic robots rather than discrete agent movements with uniform velocity, and is complete for wellformed MAPD instances. We demonstrate its benefits for automated warehouses using both an agent simulator and a standard robot simulator. For example, we demonstrate that it can compute paths for hundreds of agents and thousands of tasks in seconds and is more efficient and effective than existing MAPD algorithms that use a post-processing step to adapt their paths to continuous agent movements with given velocities.

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-driven combinatorial search framework. In a variety of empirical comparisons, we demonstrate state-of-the-art solution qualities and success rates, often with similar runtimes to existing algorithms. We also develop new theoretical results that explore the limitations of prioritized planning, in terms of completeness and optimality, for the first time.

We describe a new way of reasoning about symmetric collisions for Multi-Agent Path Finding (MAPF) on 4-neighbor grids. We also introduce a symmetry-breaking constraint to resolve these conflicts. This specialized technique allows us to identify and eliminate, in a single step, all permutations of two currently assigned but incompatible paths. Each such permutation has exactly the same cost as a current path, and each one results in a new collision between the same two agents. We show that the addition of symmetry-breaking techniques can lead to an exponential reduction in the size of the search space of CBS, a popular framework for MAPF, and report significant improvements in both runtime and success rate versus CBSH and EPEA* – two recent and state-of-the-art MAPF algorithms.

Multi-Agent Path Finding (MAPF) has been widely studied in the AI community. For example, Conflict-Based Search (CBS) is a state-of-the-art MAPF algorithm based on a twolevel tree-search. However, previous MAPF algorithms assume that an agent occupies only a single location at any given time, e.g., a single cell in a grid. This limits their applicability in many real-world domains that have geometric agents in lieu of point agents. Geometric agents are referred to as “large” agents because they can occupy multiple points at the same time. In this paper, we formalize and study LAMAPF, i.e., MAPF for large agents. We first show how CBS can be adapted to solve LA-MAPF. We then present a generalized version of CBS, called Multi-Constraint CBS (MCCBS), that adds multiple constraints (instead of one constraint) for an agent when it generates a high-level search node. We introduce three different approaches to choose such constraints as well as an approach to compute admissible heuristics for the high-level search. Experimental results show that all MC-CBS variants outperform CBS by up to three orders of magnitude in terms of runtime. The best variant also outperforms EPEA* (a state-of-the-art A*-based MAPF solver) in all cases and MDD-SAT (a state-of-the-art reduction-based MAPF solver) in some cases.

In this paper, we define Jump Point Graphs (JP), a preprocessing-based path-planning technique similar to Subgoal Graphs (SG). JP allows for the first time the combination of Jump Point Search style pruning in the context of abstraction-based speedup techniques, such as Contraction Hierarchies. We compare JP with SG and its variants and report new state-of-the-art results for grid-based pathfinding.

Conflict-Based Search (CBS) and its enhancements are among the strongest algorithms for Multi-Agent Path Finding. Recent work introduced an admissible heuristic to guide the high-level search of CBS. In this work, we prove the limitation of this heuristic, as it is based on cardinal conflicts only. We then introduce two new admissible heuristics by reasoning about the pairwise dependencies between agents. Empirically, CBS with either new heuristic significantly improves the success rate over CBS with the recent heuristic and reduces the number of expanded nodes and runtime by up to a factor of 50.

The Multi-Agent Pickup and Delivery (MAPD) problem models applications where a large number of agents attend to a stream of incoming pickup-and-delivery tasks. Token Passing (TP) is a recent MAPD algorithm that is efficient and effective. We make TP even more efficient and effective by using a novel combinatorial search algorithm, called Safe Interval Path Planning with Reservation Table (SIPPwRT), for single-agent path planning. SIPPwRT uses an advanced data structure that allows for fast updates and lookups of the current paths of all agents in an online setting. The resulting MAPD algorithm TP-SIPPwRT takes kinematic constraints of real robots into account directly during planning, computes continuous agent movements with given velocities that work on non-holonomic robots rather than discrete agent movements with uniform velocity, and is complete for well-formed MAPD instances. We demonstrate its benefits for automated warehouses using both an agent simulator and a standard robot simulator. For example, we demonstrate that it can compute paths for hundreds of agents and thousands of tasks in seconds and is more efficient and effective than existing MAPD algorithms that use a post-processing step to adapt their paths to continuous agent movements with given velocities. This paper was published at AAAI 2019.

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-driven combinatorial search framework. In a variety of empirical comparisons, we demonstrate state-of-the-art solution qualities and success rates, often with similar runtimes to existing algorithms. We also develop new theoretical results that explore the limitations of prioritized planning, in terms of completeness and optimality, for the first time. This paper was published at AAAI 2019.

Multi-Agent Motion Planning (MAMP) is the task of finding conflict-free kinodynamically feasible plans for agents from start to goal states. While MAMP is of significant practical importance, existing solvers are either incomplete, inefficient or rely on simplifying assumptions. For example, Multi-Agent Path Finding (MAPF) solvers conventionally assume discrete timesteps and rectilinear movement of agents between neighboring vertices of a graph. In this paper, we develop MAMP solvers that obviate these simplifying assumptions and yet generalize the core ideas of state-of-the-art MAPF solvers. Specifically, since different motions may take arbitrarily different durations, MAMP solvers need to efficiently reason with continuous time and arbitrary wait durations. To do so, we adapt (Enhanced) Conflict-Based Search to continuous time and develop a novel bounded-suboptimal extension of Safe Interval Path Planning, called Soft Conflict Interval Path Planning. On the theoretical side, we justify the completeness, optimality and bounded-suboptimality of our MAMP solvers. On the experimental side, we show that our MAMP solvers scale well with increasing suboptimality bounds.

Conflict-Based Search (CBS) and its enhancements are among the strongest algorithms for Multi-Agent Pathfinding. Recent work introduced an admissible heuristic to guide the high-level search of CBS. In this work, we prove the limitation of this heuristic, as it is based on cardinal conflicts only. We then introduce two new admissible heuristics by reasoning about the pairwise dependency between agents. Empirically, CBS with both new heuristics significantly improves the success rate over CBS with the recent heuristic and reduces the number of expanded nodes and runtime by up to a factor of 50, yielding a new state-of-the-art CBS-based algorithm.

We describe a new way of reasoning about symmetric collisions for Multi-Agent Path Finding (MAPF) on 4-neighbor grids. We also introduce a symmetry-breaking constraint to resolve these conflicts. This specialized technique allows us to identify and eliminate, in a single step, all permutations of two currently assigned but incompatible paths. Each such permutation has exactly the same cost as a current path, and each one results in a new collision between the same two agents. We show that the addition of symmetry-breaking techniques can lead to an exponential reduction in the size of the search space of CBS, a popular framework for MAPF, and report significant improvements in both runtime and success rate versus CBSH and EPEA* – two recent and state-of-the-art MAPF algorithms.

Multi-Agent Path Finding (MAPF) has been widely studied in the AI community. For example, Conflict-Based Search (CBS) is a state-of-the-art MAPF algorithm based on a two-level tree-search. However, previous MAPF algorithms assume that an agent occupies only a single location at any given time, e.g., a single cell in a grid. This limits their applicability in many real-world domains that have geometric agents in lieu of point agents. Geometric agents are referred to as “large” agents because they can occupy multiple points at the same time. In this paper, we formalize and study LAMAPF, i.e., MAPF for large agents. We first show how CBS can be adapted to solve LA-MAPF. We then present a generalized version of CBS, called Multi-Constraint CBS (MC-CBS), that adds multiple constraints (instead of one constraint) for an agent when it generates a high-level search node. We introduce three different approaches to choose such constraints as well as an approach to compute admissible heuristics for the high-level search. Experimental results show that all MC-CBS variants outperform CBS by up to three orders of magnitude in terms of runtime. The best variant also outperforms EPEA* (a state-of-the-art A*-based MAPF solver) in all cases and MDD-SAT (a state-of-the-art reduction-based MAPF solver) in some cases.

The multi-agent pathfinding problem (MAPF) is the fundamental problem of planning paths for multiple agents, where the key constraint is that the agents will be able to follow these paths concurrently without colliding with each other. Applications of MAPF include automated warehouses, autonomous vehicles, and robotics. Research on MAPF has been flourishing in the past couple of years. Different MAPF research papers assume different sets of assumptions, e.g., whether agents can traverse the same road at the same time, and have different objective functions, e.g., minimize makespan or sum of agents' actions costs. These assumptions and objectives are sometimes implicitly assumed or described informally. This makes it difficult for establishing appropriate baselines for comparison in research papers, as well as making it difficult for practitioners to find the papers relevant to their concrete application. This paper aims to fill this gap and facilitate future research and practitioners by providing a unifying terminology for describing the common MAPF assumptions and objectives. In addition, we also provide pointers to two MAPF benchmarks. In particular, we introduce a new grid-based benchmark for MAPF, and demonstrate experimentally that it poses a challenge to contemporary MAPF algorithms.

Many existing boundedly-suboptimal heuristic search algorithms are variants of best-first search. Due to memory limitations, these algorithms are unable to solve problems with extremely large search spaces. In this paper, we present a framework that allows best-first search algorithms to solve problems with such large search spaces given a (reasonable) memory bound while also preserving optimality guarantees in tree-structured search spaces. In our framework, a given algorithm is run several times. In each search episode, the algorithm expands up to a user-defined number of states. After each episode, unless the goal has been found, the heuristic values of the generated states are updated using a linear-time algorithm that preserves consistency in tree-structured search spaces. In subsequent search episodes, only the heuristic values of the states generated in the previous episode need to be kept in memory. We present experimental results where we plug A*, GBFS, and wA* into our framework to solve traveling salesman problems and compare them against benchmark linear-memory algorithms like DFBnB and wDFBnB.

Planning smooth trajectories is important for the safe, efficient and comfortable operation of mobile robots, such as wheeled robots moving in crowded environments or cars moving at high speed. Asymptotically optimal sampling-based motion planners can be used to generate such trajectories. However, to achieve the necessary efficiency for the realtime operation of robots, one often uses their initial feasible trajectories or the trajectories of non-optimal motion planners instead, typically after a post-smoothing step. We propose a gradient-informed post-smoothing algorithm, called GRIPS, that deforms given trajectories by locally optimizing the placement of vertices while satisfying the system's kinodynamic constraints. We show experimentally that GRIPS typically produces trajectories of significantly smaller length and higher smoothness than several existing post-smoothing algorithms.

We formalize Multi-Agent Path Finding with Deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within the deadline, without colliding with each other. We first show that MAPF-DL is NP-hard to solve optimally. We then present two classes of optimal algorithms, one based on a reduction of MAPF-DL to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network and the other one based on novel combinatorial search algorithms. Our empirical results demonstrate that these MAPF-DL solvers scale well and each one dominates the other ones in different scenarios.

Focal search (FS) is a bounded-suboptimal search (BSS) variant of A*. Like A*, it uses an open list whose states are sorted in increasing order of their f-values. Unlike A*, it also uses a focal list containing all states from the open list whose f-values are no larger than a suboptimality factor times the smallest f-value in the open list. In this paper, we develop an anytime version of FS, called anytime FS (AFS), that is useful when deliberation time is limited. AFS finds a "good" solution quickly and refines it to better and better solutions if time allows. It does this refinement efficiently by reusing previous search efforts. On the theoretical side, we show that AFS is bounded suboptimal and that anytime potential search (ATPS/ANA*), a state-of-the-art anytime bounded-cost search (BCS) variant of A*, is a special case of AFS. In doing so, we bridge the gap between anytime search algorithms based on BSS and BCS. We also identify different properties of priority functions, used to sort the focal list, that may allow for efficient reuse of previous search efforts. On the experimental side, we demonstrate the usefulness of AFS for solving hard combinatorial problems, such as the generalized covering traveling salesman problem and the multi-agent pathfinding problem.

We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph. Later, at runtime, a shortest path between any two nodes can be computed with an A* search using the Euclidean distances as heuristic. Our preprocessing algorithm, called FastMap, is inspired by the data-mining algorithm of the same name and runs in near-linear time. Hence, FastMap is orders of magnitude faster than competing approaches that produce a Euclidean embedding using Semidefinite Programming. FastMap also produces admissible and consistent heuristics and therefore guarantees the generation of shortest paths. Moreover, FastMap applies to general undirected graphs for which many traditional heuristics, such as the Manhattan Distance heuristic, are not well defined. Empirically, we demonstrate that A* search using the FastMap heuristic is competitive with A* search using other state-of-the-art heuristics, such as the Differential heuristic.

Contraction hierarchies and (N-level) subgoal graphs are two preprocessing-based path-planning algorithms that have so far only been compared experimentally through the grid-based path-planning competitions, where both algorithms had undominated runtime/memory trade-offs. Subgoal graphs can be considered as a framework that can be customized to different domains through the choice of a reachability relation R that identifies pairs of nodes on a graph between which it is easy to find shortest paths. Subgoal graphs can exploit R in various ways to speed-up query times and reduce memory requirements. In this paper, we break down the differences between N-level subgoal graphs and contraction hierarchies, and augment contraction hierarchies with ideas from subgoal graphs to exploit R. We propose three different modifications, analyze their runtime/memory trade-offs, and provide experimental results on grids using canonical-freespace-reachability as R, which show that both N-level subgoal graphs and contraction hierarchies are dominated in terms of the runtime/memory trade-off by some of our new variants.

Multi-Agent Path Finding (MAPF) is an NP-hard problem that has been well studied in artificial intelligence and robotics. Recently, randomized MAPF solvers have been shown to exhibit heavy-tailed distributions of runtimes, which can be exploited to boost their success rate for a given runtime limit. In this paper, we discuss different ways of randomizing MAPF solvers and evaluate simple rapid randomized restart strategies for state-of-the-art MAPF solvers such as iECBS, M* with highways and CBS-CL.

Subgoal graphs can be constructed on top of graphs during a preprocessing phase to speed-up shortest path queries. They have an undominated query-time/memory trade-off in the Grid-Based Path Planning Competitions. While grids are useful for path planning, other kinds of graphs, such as state lattices, have to be used for motion planning. While state lattices are regular graphs like grids, subgoal graphs improve query times by a much smaller factor on state lattices than on grids. In this paper, we present a new version of subgoal graphs that forfeits its optimality guarantee for smaller query times. It guarantees completeness, and our experimental results on state lattices suggest that it can find paths that are close to optimal.

Local consistency algorithms, like arc consistency (AC) algorithms, are polynomial-time algorithms that prune the search space of constraint satisfaction problems (CSPs). In this paper, we present connections between message passing algorithms and AC for semiring-based CSPs (SCSPs) and valued CSPs (VCSPs), two well-established frameworks that generalize CSPs. Message passing algorithms are well known distributed search algorithms for solving many combinatorial problems in artificial intelligence, probabilistic reasoning, and information theory. However, the relationship between message passing algorithms and SCSPs or VCSPs still remains understudied. Towards this end, we propose the best-O message passing (BOMP) algorithm for SCSPs and VCSPs. We prove that, unlike other standard message passing algorithms which are in general not guaranteed to converge, the BOMP algorithm guarantees convergence for SCSPs and specific subclasses of VCSPs. We also theoretically study the relationship between the BOMP algorithm and AC on SCSPs, and empirically study the quality of the solutions produced by the BOMP algorithm for VCSPs.

Several recently developed Multi-Agent Path Finding (MAPF) solvers scale to large MAPF instances by searching for MAPF plans on 2 levels: The high-level search resolves collisions between agents, and the low-level search plans paths for single agents under the constraints imposed by the high-level search. We make the following contributions to solve the MAPF problem with imperfect plan execution with small average makespans: First, we formalize the MAPF Problem with Delay Probabilities (MAPF-DP), define valid MAPF-DP plans and propose the use of robust plan-execution policies for valid MAPF-DP plans to control how each agent proceeds along its path. Second, we discuss 2 classes of decentralized robust plan-execution policies (called Fully Synchronized Policies and Minimal Communication Policies) that prevent collisions during plan execution for valid MAPF-DP plans. Third, we present a 2-level MAPF-DP solver (called Approximate Minimization in Expectation) that generates valid MAPF-DP plans.

Multi-Agent Path Finding (MAPF) is well studied in both AI and robotics. Given a discretized environment and agents with assigned start and goal locations, MAPF solvers from AI find collision-free paths for hundreds of agents with user-provided sub-optimality guarantees. However, they ignore that actual robots are subject to kinematic constraints (such as velocity limits) and suffer from imperfect plan-execution capabilities. We therefore introduce MAPF-POST to postprocess the output of a MAPF solver in polynomial time to create a plan-execution schedule that can be executed on robots. This schedule works on non-holonomic robots, considers kinematic constraints, provides a guaranteed safety distance between robots, and exploits slack to avoid time-intensive replanning in many cases. We evaluate MAPF-POST in simulation and on differential-drive robots, showcasing the practicality of our approach.

Search using subgoal graphs is a recent preprocessing-based path-planning algorithm that can find shortest paths on 8-neighbor grids several orders of magnitude faster than A*, while requiring little preprocessing time and memory overhead. In this paper, we first generalize the ideas behind subgoal graphs to a framework that can be specialized to different types of environments (represented as weighted directed graphs) through the choice of a reachability relation. Intuitively, a reachability relation identifies pairs of vertices for which a shortest path can be found quickly. A subgoal graph can then be constructed as an overlay graph that is guaranteed to have edges only between vertices that satisfy the reachability relation, which allows one to find shortest paths on the original graph quickly. In the context of this general framework, subgoal graphs on grids use freespace-reachability (originally called h-reachability) as the reachability relation, which holds for pairs of vertices if and only if their distance on the grid with blocked cells is equal to their distance on the grid without blocked cells (freespace assumption). We apply this framework to state lattices by using variants of freespace-reachability as the reachability relation. We provide preliminary results on (x,y,theta)-state lattices, which shows that subgoal graphs can be used to speed up path planning on state lattices as well, although the speed-up is not as significant as it is on grids.

In this paper, we develop the message passing based linear-time and linear-space MVC algorithm (MVC-MPL) for solving the minimum vertex cover (MVC) problem. MVC-MPL is based on heuristics derived from a theoretical analysis of message passing algorithms in the context of belief propagation. We show that MVC-MPL produces smaller vertex covers than other linear-time and linear-space algorithms.

We study transportation problems where robots have to deliver packages and can transfer the packages among each other. Specifically, we study the package-exchange robot-routing problem (PERR), where each robot carries one package, any two robots in adjacent locations can exchange their packages, and each package needs to be delivered to a given destination. We prove that exchange operations make all PERR instances solvable. Yet, we also show that PERR is NP-hard to approximate within any factor less than 4/3 for makespan minimization and is NP-hard to solve for flowtime minimization, even when there are only two types of packages. Our proof techniques also generate new insights into other transportation problems, for example, into the hardness of approximating optimal solutions to the standard multi-agent path-finding problem (MAPF). Finally, we present optimal and suboptimal PERR solvers that are inspired by MAPF solvers, namely a flow-based ILP formulation and an adaptation of conflict-based search. Our empirical results demonstrate that these solvers scale well and that PERR instances often have smaller makespans and flowtimes than the corresponding MAPF instances.

RRT and RRT* have become popular planning techniques, in particular for high-dimensional systems such as wheeled robots with complex nonholonomic constraints. Their planning times, however, can scale poorly for such robots, which has motivated researchers to study hierarchical techniques that grow the RRT trees in more focused ways. Along this line, we introduce Theta*-RRT that hierarchically combines (discrete) any-angle search with (continuous) RRT motion planning for nonholonomic wheeled robots. Theta*-RRT is a variant of RRT that generates a trajectory by expanding a tree of geodesics toward sampled states whose distribution summarizes geometric information of the any-angle path. We show experimentally, for both a differential drive system and a high-dimensional truck-and-trailer system, that Theta*-RRT finds shorter trajectories significantly faster than four baseline planners (RRT, A*-RRT, RRT*, A*-RRT*) without loss of smoothness, while A*-RRT* and RRT* (and thus also Informed RRT*) fail to generate a first trajectory sufficiently fast in environments with complex nonholonomic constraints. We also prove that Theta*-RRT retains the probabilistic completeness of RRT for all small-time controllable systems that use an analytical steer function.

In this paper, we study the Complex Routing Problem (CRP), where several homogeneous robots need to visit given task locations to accomplish complex tasks in a cooperative setting. Each task location hosts a task. The complexity level of a task is defined as the number of robots that need to be simultaneously present at its location to accomplish it. The robots need to be routed so that all tasks get accomplished with minimal makespan. We present a new centralized algorithm, called SAGL, for solving the CRP heuristically. SAGL is inspired by the application of linear programming duality to the Steiner Forest Problem. It makes less restrictive assumptions than the state-of-the-art distributed Approach with Reaction Functions and scales better in both the complexity levels of tasks and the number of complex tasks (whose complexity levels are greater than one), although it results in somewhat larger makespans.

We study formation change for robot groups in known environments. We are given a team of robots partitioned into groups, where robots in the same group are interchangeable with each other. A formation specifies the locations occupied by each group. The objective is to find collision-free paths that move all robots from a given start formation to a given goal formation. Our algorithm TAPF* has the following features: (a) it incorporates kinematic constraints of robots in form of velocity limits; (b) it maintains a user-specified safety distance between robots; (c) it attempts to minimize the makespan; and (d) it runs efficiently for hundreds of robots and dozens of groups even in dense 3D environments with narrow corridors and other occlusions. We demonstrate the efficiency and effectiveness of TAPF* in simulation and on robots.

Multi-agent path-finding (MAPF) is important for applications such as the kind of warehousing done by Kiva systems. Solving the problem optimally is NP-hard, yet finding low-cost solutions is important. Bounded-suboptimal MAPF algorithms, such as enhanced conflict-based search (ECBS), often do not perform well in warehousing domains with many agents. We therefore develop bounded-suboptimal MAPF algorithms, called CBS+HWY and ECBS+HWY, that exploit the problem structure of a given MAPF instance by finding paths for the agents that include edges from user-provided highways, which encourages a global behavior of the agents that avoids collisions. On the theoretical side, we develop a simple approach that uses highways for MAPF and provides suboptimality guarantees. On the experimental side, we demonstrate that ECBS+HWY can decrease the runtimes and solution costs of ECBS in Kiva-like domains with many agents if the highways capture the problem structures well.

The Grid-Based Path Planning Competition has just completed its third iteration. The entriesused in the competition have improved significantly during this time, changing the view ofthe state of the art of grid-based pathfinding. Furthermore, the entries from the competition have beenmade publicly available, improving the ability of researchers to compare their work. Thispaper summarizes the entries to the 2014 competition, presents the 2014 competition results,and talks about what has been learned and where there is room for improvement.

We compare five any-angle path-planning algorithms, Theta*, Block A*, Field D*, ANYA, and Any-Angle Subgoal Graphs in terms of solution quality and runtime. Any-angle path-planning is a fairly new research area, and no direct comparison exists between these algorithms. We implement each algorithm from scratch and use similar implementations to provide a fair comparison.

Demand-responsive transport (DRT) systems provide flexible transport services for passengers who request door-to-door rides in shared-ride mode without fixed routes and schedules. DRT systems face interesting coordination challenges. For example, one has to design cost-sharing mechanisms for offering fare quotes to potential passengers so that all passengers are treated fairly. The main issue is how the operating costs of the DRT system should be shared among the passengers (given that different passengers cause different amounts of inconvenience to the other passengers), taking into account that DRT systems should provide fare quotes instantaneously without knowing future ride request submissions. We determine properties of cost-sharing mechanisms that make DRT systems attractive to both the transport providers and passengers, namely online fairness, immediate response, individual rationality, budget balance, and ex-post incentive compatibility. We propose a novel cost-sharing mechanism, which is called Proportional Online Cost Sharing (POCS), which provides passengers with upper bounds on their fares immediately after their ride request submissions despite missing knowledge of future ride request submissions, allowing them to accept their fare quotes or drop out. We examine how POCS satisfies these properties in theory and computational experiments.

In this paper, we describe a simple randomized algorithm that runs in polynomial time and solves connected row convex (CRC) constraints in distributed settings. CRC constraints generalize many known tractable classes of constraints like 2-SAT and implicational constraints. They can model problems in many domains including temporal reasoning and geometric reasoning, and generally speaking, play the role of ``Gaussians'' in the logical world. Our simple randomized algorithm for solving them in distributed settings, therefore, has a number of important applications. We support our claims through a theoretical analysis and empirical results.

Search with Subgoal Graphs (Uras, Koenig, and Hernandez 2013) was a non-dominated optimal path-planning algorithm in the Grid-Based Path Planning Competitions 2012 and 2013. During a preprocessing phase, it computes a Simple Subgoal Graph from a given grid, which is analogous to a visibility graph for continuous terrain, and then partitions the vertices into global and local subgoals to obtain a Two-Level Subgoal Graph. During the path-planning phase, it performs an A* search that ignores local subgoals that are not relevant to the search, which significantly reduces the size of the graph being searched. In this paper, we generalize this partitioning process to any undirected graph and show that it can be recursively applied to generate more than two levels, which reduces the size of the graph being searched even further. We distinguish between basic partitioning, which only partitions the vertices into different levels, and advanced partitioning, which can also add new edges.We show that the construction of Simple-Subgoal Graphs from grids and the construction of Two-Level Subgoal Graphs from Simple Subgoal Graphs are instances of generalized partitioning. We then report on experiments on Subgoal Graphs that demonstrate the effects of different types and levels of partitioning. We also report on experiments that demonstrate that our new N-Level Subgoal Graphs achieve a speed up of 1.6 compared to Two-Level Subgoal graphs from (Uras, Koenig, and Hern´andez 2013) on maps from the video games StarCraft and Dragon Age: Origins.

Coordinating fleets of autonomous, non-holonomic vehicles is paramount to many industrial applications. While there exists solutions to efficiently calculate trajectories for individual vehicles, an effective methodology to coordinate their motions and to avoid deadlocks is still missing. Decoupled approaches, where motions are calculated independently for each vehicle and then centrally coordinated for execution, have the means to identify deadlocks, but not to solve all of them. We present a novel approach that overcomes this limitation and that can be used to complement the deficiencies of decoupled solutions with centralized coordination. Here, we formally define an extension of the framework of lattice-based motion planning to multi-robot systems and we validate it experimentally. Our approach can jointly plan for multiple vehicles and it generates kinematically feasible and deadlock-free motions.

Abstracts of the invited talks presented at SoCS 2014.

For some search problems, the graph is known beforehand and there is time to preprocess the graph to make the search faster. One such example is video games, where one can often preprocess maps before a game is released or while a map is loaded into memory. The data produced by preprocessing should use only a small amount of memory, and, in case they are generated during runtime, preprocessing should be fast. Search with Subgoal Graphs (Uras, Koenig, and Hernandez 2013) was a non-dominated optimal path-planning algorithm in the Grid-Based Path Planning Competitions 2012 and 2013. During a preprocessing phase, it computes a Simple Subgoal Graph from a given grid, which is analogous to a visibility graph for continuous terrain, and then partitions the vertices into global and local subgoals to obtain a Two-Level Subgoal Graph. During the path-planning phase, it performs an A* search over the subgoal graph that ignores local subgoals that are not relevant to the search, which significantly reduces the size of the graph being searched. This paper is an abstract of (Uras and Koenig 2014), which generalizes this partitioning process to any undirected graph and shows that it can be recursively applied to generate more than two levels, which reduces the size of the graph being searched even further. We call these graphs N-Level Graphs.

In this paper, we define and study the general framework of Simple Temporal Problems with Taboo regions (STPTs) and show how these problems capture metric temporal reasoning aspects which are common to many real-world applications. STPTs encode simple temporal constraints between events and user-defined taboo regions on the timeline, during which no event is allowed to take place. We discuss two different variants of STPTs. The first one deals with (instantaneous) events, while the second one allows for (durative) processes. We also provide polynomial-time algorithms for solving them. If all events or processes cannot be scheduled outside of the taboo regions, one needs to define and reason about "soft" STPTs. We show that even "soft" STPTs can be solved in polynomial time, using reductions to max-flow problems. The resulting algorithms allow for incremental computations, which is important for the successful application of our approach in real-time domains.

Incremental search algorithms, such as D* Lite, reuse information from previous searches to speed up the current search and can thus solve sequences of similar search problems faster than Repeated A*, which performs repeated A* searches. In this position paper, we study goal-directed navigation in initially unknown terrain and point out that it is currently not well understood when D* Lite runs faster than Repeated A*. In general, it appears that Repeated A* runs faster than D* Lite for easy navigation problems (where the agent reaches the goal with only a small number of searches), which means that it runs faster than D* Lite quite often in practice. We draw two conclusions, namely that incremental search algorithms need to be evaluated in more diverse testbeds to improve our understanding of their properties and that they can be improved to be more competitive for easy navigation problems.

This paper summarizes our AAMAS 2012 paper on "Time-Bounded Adaptive A*," which introduces the game time model to evaluate search algorithms in real-time settings, such as video games. It then extends the existing real-time search algorithm TBA* to path planning with the freespace assumption in initially partially or completely unknown terrain, resulting in Time-Bounded Adaptive A* (TBAA*). TBAA* needs fewer time intervals in the game time model than several state-of-the-art complete and real-time search algorithms and about the same number of time intervals as the best compared complete search algorithm, even though it has the advantage over complete search algorithms that the agent starts to move right away.

We propose a method for preprocessing an eight-neighbor gridworld to generate a subgoal graph and a method for using this subgoal graph to find shortest paths faster than A*, by first finding high-level paths through subgoals and then shortest low-level paths between consecutive subgoals on the high-level path.

We study distributed task-allocation problems where cooperative agents need to perform some tasks simultaneously. Examples are multi-agent routing problems where several agents need to visit some targets simultaneously, for example, to move obstacles out of the way cooperatively. In this paper, we first generalize the concept of reaction functions proposed in the literature to characterize the agent costs of performing multiple complex tasks. Second, we show how agents can construct and approximate reaction functions in a distributed way. Third, we show how reaction functions can be used by an auctionlike algorithm to allocate tasks to agents. Finally, we show empirically that the team costs of our algorithms are substantially smaller than those of an existing state-of-the-art allocation algorithm for complex tasks.

Auctions are promising decentralized methods for teams of agents to allocate and re-allocate tasks among themselves in dynamic, partially known and time-constrained domains with positive or negative synergies among tasks. Auction-based coordination systems are easy to understand, simple to implement and broadly applicable. They promise to be efficient both in communication (since agents communicate only essential summary information) and in computation (since agents compute their bids in parallel). Artificial intelligence research has explored auction-based coordination systems since the early work on contract networks, mostly from an experimental perspective. This overview paper describes our recent progress towards creating a framework for the design and analysis of cooperative auctions for agent coordination.

Grids with blocked and unblocked cells are often used to represent continuous 2D and 3D environments in robotics and video games. The shortest paths formed by the edges of 8-neighbor 2D grids can be up to 8% longer than the shortest paths in the continuous environment. Theta* typically finds much shorter paths than that by propagating information along graph edges (to achieve short runtimes) without constraining paths to be formed by graph edges (to find short "any-angle" paths). We show in this paper that the shortest paths formed by the edges of 26-neighbor 3D grids can be 13% longer than the shortest paths in the continuous environment, which highlights the need for smart path planning algorithms in 3D. Theta* can be applied to 3D grids in a straight-forward manner, but it performs a line-of-sight check for each unexpanded visible neighbor of each expanded vertex and thus it performs many more line-of-sight checks per expanded vertex on a 26-neighbor 3D grid than on an 8-neighbor 2D grid. We therefore introduce Lazy Theta*, a variant of Theta* which uses lazy evaluation to perform only one line-of-sight check per expanded vertex (but with slightly more expanded vertices). We show experimentally that Lazy Theta* finds paths faster than Theta* on 26-neighbor 3D grids, with one order of magnitude fewer line-of-sight checks and without an increase in path length.

We study the distributed allocation of tasks to cooperating robots in real time, where each task has to be assigned to exactly one robot so that the sum of the latencies of all tasks is as small as possible. We propose a new auction-like algorithm, called Sequential Incremental-Value (SIV) auction, which assigns tasks to robots in multiple rounds. The idea behind SIV auctions is to assign as many tasks per round to robots as possible as long as their individual costs for performing these tasks are at most a given bound, which increases exponentially from round to round. Our theoretical results show that the team costs of SIV auctions are at most a constant factor larger than minimal.

Almost no research has been done on designing pinball games although much research has been done on designing video games. We are interested in designing pinball games on pinball machines to teach computer science students about how to interface to mechanical systems in a fun and motivating way. Thus, we have developed a pinball machine interface between a PC and a recent Lord of the Rings pinball machine. We demonstrate that it is easy to innovate pinball games by designing and implementing Pinhorse, a pinball game that avoids some of the design problems of existing pinball games. For example, it features a true multiplayer mode where each player directly influences the game of the other player within a limited amount of play time. This paper describes both our innovative pinball game and the hardware and software of our pinball machine interface that enables game designers to develop such pinball games on real pinball machines.

Grids with blocked and unblocked cells are often used to represent continuous 2D and 3D environments in robotics and video games. The shortest paths formed by the edges of 8-neighbor 2D grids can be up to ≈ 8% longer than the shortest paths in the continuous environment. Theta* typically finds much shorter paths than that by propagating information along graph edges (to achieve short runtimes) without constraining paths to be formed by graph edges (to find short “any-angle” paths). We show in this paper that the shortest paths formed by the edges of 26-neighbor 3D grids can be ≈ 13% longer than the shortest paths in the continuous environment, which highlights the need for smart path planning algorithms in 3D. Theta* can be applied to 3D grids in a straight-forward manner, but it performs a line-of-sight check for each unexpanded visible neighbor of each expanded vertex and thus it performs many more line-of-sight checks per expanded vertex on a 26-neighbor 3D grid than on an 8-neighbor 2D grid. We therefore introduce Lazy Theta*, a variant of Theta* which uses lazy evaluation to perform only one line-of-sight check per expanded vertex (but with slightly more expanded vertices). We show experimentally that Lazy Theta* finds paths faster than Theta* on 26-neighbor 3D grids, with one order of magnitude fewer line-of-sight checks and without an increase in path length.

Grids with blocked and unblocked cells are often used to represent terrain in robotics and video games. However, paths formed by grid edges can be longer than true shortest paths in the terrain since their headings are artificially constrained. We present two new correct and complete any-angle path-planning algorithms that avoid this shortcoming. Basic Theta* and Angle-Propagation Theta* are both variants of A* that propagate information along grid edges without constraining paths to grid edges. Basic Theta* is simple to understand and implement, fast and finds short paths. However, it is not guaranteed to find true shortest paths. Angle-Propagation Theta* achieves a better worst-case complexity per vertex expansion than Basic Theta* by propagating angle ranges when it expands vertices, but is more complex, not as fast and finds slightly longer paths. We refer to Basic Theta* and Angle-Propagation Theta* collectively as Theta*. Theta* has unique properties, which we analyze in detail. We show experimentally that it finds shorter paths than both A* with post-smoothed paths and Field D* (the only other version of A* we know of that propagates information along grid edges without constraining paths to grid edges) with a runtime comparable to that of A* on grids. Finally, we extend Theta* to grids that contain unblocked cells with non-uniform traversal costs and introduce variants of Theta* which provide different tradeoffs between path length and runtime.

Distributed constraint optimization (DCOP) problems are a popular way of formulating and solving agent-coordination problems. A DCOP problem is a problem where several agents coordinate their values such that the sum of the resulting constraint costs is minimal. It is often desirable to solve DCOP problems with memory-bounded and asynchronous algorithms. We introduce Branch-and-Bound ADOPT (BnB-ADOPT), a memory-bounded asynchronous DCOP search algorithm that uses the message-passing and communication framework of ADOPT (Modi, Shen, Tambe, & Yokoo, 2005), a well known memory-bounded asynchronous DCOP search algorithm, but changes the search strategy of ADOPT from best-first search to depth-first branch-and-bound search. Our experimental results show that BnB-ADOPT finds cost-minimal solutions up to one order of magnitude faster than ADOPT for a variety of large DCOP problems and is as fast as NCBB, a memory-bounded synchronous DCOP search algorithm, for most of these DCOP problems. Additionally, it is often desirable to find bounded-error solutions for DCOP problems within a reasonable amount of time since finding cost-minimal solutions is NP-hard. The existing bounded-error approximation mechanism allows users only to specify an absolute error bound on the solution cost but a relative error bound is often more intuitive. Thus, we present two new bounded-error approximation mechanisms that allow for relative error bounds and implement them on top of BnB-ADOPT.

Localization, which is the determination of one's location in a known terrain, is a fundamental task for autonomous robots. This paper presents several new basic theoretical results about localization. We show that, even under the idealized assumptions of accurate sensing and perfect actuation, it is intrinsically difficult to localize a robot with a travel distance that is close to minimal. Our result helps to theoretically justify the common use of fast localization heuristics, such as greedy localization, which always moves the robot to a closest informative location (where the robot makes an observation that decreases the number of its possible locations). We show that the travel distance of greedy localization is much larger than minimal in some terrains because the closest informative location can distract greedy localization from a slightly farther, but much more informative, location. However, we also show that the travel distance of greedy localization can be larger, but not much larger, than the terrain sizen. Thus, the travel distance of greedy localization scales well with the terrain size and is much larger than minimal in some terrains, not because it is large with respect to the terrain size, but because the minimal travel distance is exceptionally small in these terrains. As a corollary to our analysis, we show that the travel distance of greedy mapping (which always moves the robot to a closest location, where it makes an observation that increases its knowledge of the terrain) cannot be much larger than the terrain size. In theoretical terms, we prove the NP-hardness of minimization of travel distance for localization to within a logarithmic factor of the terrain size. We prove that the travel distance of greedy localization is at least ordern/ log2nlarger than minimal in some terrains and that it is at least ordernlogn/ log lognin the worst case. Finally, we prove that the travel distance of both greedy localization and greedy mapping is at most ordernlogn. Previously, it was only known that it is NP-hard to localize with minimal travel distance and that the travel distances of greedy localization and greedy mapping are at most ordern3/2.

One of the main applications of mobile robots is coverage: visiting each location in known terrain. Coverage is crucial for lawn mowing, cleaning, harvesting, search-and-rescue, intrusion detection, and mine clearing. Naturally, coverage can be sped up with multiple robots. However, we show that solving several versions of multirobot coverage problems with minimal cover times is NP-hard, which provides motivation for designing polynomial-time constant-factor approximation algorithms. We then describe multirobot forest coverage (MFC), a new polynomial-time multirobot coverage algorithm based on an algorithm by Even et al. [Min-max tree covers of graphs. Oper. Res. Lett., vol. 32, pp. 309-315, 2004] for finding a tree cover with trees of balanced weights. Our theoretical results show that the cover times of MFC in weighted and unweighted terrain are at most about a factor of 16 larger than minimal. Our simulation results show that the cover times of MFC are close to minimal in all tested scenarios and smaller than the cover times of an alternative multirobot coverage algorithm.

We study multi-robot routing problems (MR-LDR) where a team of robots has to visit a set of given targets with linear decreasing rewards over time, such as required for the delivery of goods to rescue sites after disasters. The objective of MR-LDR is to find an assignment of targets to robots and a path for each robot that maximizes the surplus, which is defined to be the total reward collected by the team minus its total travel cost. We develop a mixed integer program that solves MR-LDR optimally with a flow-type formulation and can be solved faster than the standard TSP-type formulations but also show that solving MR-LDR optimally is NP-hard. We then develop an auction-based algorithm and demonstrate that it solves MR-LDR in seconds and with a surplus that is comparable to the surplus found by the mixed integer program with a 12 hour time limit.

We study task-allocation problems where cooperative robots need to perform tasks simultaneously. We develop a distributed negotiation procedure that allows robots to find all task exchanges that reduce the team cost of a given task allocation, without robots having to know how other robots compute their robot costs. Finally, we demonstrate empirically that our negotiation procedure can substantially reduce the team costs of task allocations resulting from existing task-allocation procedures, including sequential single-item auctions.

Localization is a fundamental problem in robotics. The “kidnapped robot” possesses a compass and map of its environment; it must determine its location at a minimum cost of travel distance. The problem is NP-hard [G. Dudek, K. Romanik, and S. Whitesides, SIAM J. Comput., 27 (1998), pp. 583–604] even to minimize within factor $c\log n$ [C. Tovey and S. Koenig, Proceedings of the National Conference on Artificial Intelligence, Austin, TX, 2000, pp. 819–824], where n is the map size. No approximation algorithm has been known. We give an $O(\log^3n)$-factor algorithm. The key idea is to plan travel in a “majority-rule” map, which eliminates uncertainty and permits a link to the $\frac{1}{2}$-Group Steiner (not Group Steiner) problem. The approximation factor is not far from optimal: we prove a $c\log^{2-\epsilon}n$ lower bound, assuming $NP\not\subseteq ZTIME(n^{polylog(n)})$, for the grid graphs commonly used in practice. We also extend the algorithm to polygonal maps by discretizing the problem using novel geometric techniques.

Multiple robots are often faster and more fault- tolerant than single robots for applications such as planetary exploration and search and rescue. We study applications where robots move in two-dimensional terrain and have to visit targets of given priorities during given time windows that do not overlap. We analyze the complexity of these coordination tasks and, where possible, use techniques from operations research to develop coordination methods that are efficient and optimize the team performance. We then develop auction-based coordination methods that build on these results and show experimentally that they run in seconds and achieve good team performance for NP-hard coordination tasks.

In this paper, we study how multiple robots can cover known terrain quickly. We extend Multi-Robot Forest Coverage, a state-of-the-art multi-robot coverage algorithm, from terrain with uniform traversability to terrain with nonuniform traversability, which is nontrivial. We prove that its cover times are at most about sixteen times larger than minimal and demonstrate experimentally that they are significantly smaller than those of an alternative multi-robot coverage algorithm.

We study how to improve sequential single-item auctions that assign targets to robots for exploration tasks such as environmental clean-up, space-exploration, and search and rescue missions. We exploit the insight that the resulting travel distances are small if the bidding and winner-determination rules are designed to result in hillclimbing, namely to assign an additional target to a robot in each round of the sequential single-item auction so that the team cost increases the least. We study the impact of increasing the lookahead of hillclimbing and using roll-outs to improve the evaluation of partial target assignments. We describe the bidding and winner-determination rules of the resulting sequential single-item auctions and evaluate them experimentally, with surprising results: larger lookaheads do not improve sequential single-item auctions reliably while only a small number of roll-outs in early rounds already improve them substantially

One of the main applications of mobile robots is terrain coverage: visiting each location in known terrain. Terrain coverage is crucial for lawn mowing, cleaning, harvesting, search-and-rescue, intrusion detection and mine clearing. Naturally, coverage can be sped up with multiple robots. In this paper, we describe multi-robot forest coverage, a new multi-robot coverage algorithm based on an algorithm by Even et al. (2004) for finding a tree cover with trees of balanced weights. The cover time of multi-robot forest coverage is at most eight times larger than optimal, and our experiments show it to perform significantly better than existing multi-robot coverage algorithms.

D* is a greedy heuristic planning method that is widely used in robotics, including several Nomad class robots and the Mars rover prototype, to reach a destination in unknown terrain. We obtain nearly sharp lower and upper bounds of $\Omega(n\log n/\log\log n)$ and O(n log n), respectively, on the worst-case total distance traveled by the robot, for the grid graphs on n vertices typically used in robotics applications. For arbitrary graphs we prove an O(n log 2 n ) upper bound.

Mobile robots often operate in domains that are only incompletely known, for example, when they have to move from given start coordinates to given goal coordinates in unknown terrain. In this case, they need to be able to replan quickly as their knowledge of the terrain changes. Stentz' Focussed Dynamic A/sup */ (D/sup */) is a heuristic search method that repeatedly determines a shortest path from the current robot coordinates to the goal coordinates while the robot moves along the path. It is able to replan faster than planning from scratch since it modifies its previous search results locally. Consequently, it has been extensively used in mobile robotics. In this article, we introduce an alternative to D/sup */ that determines the same paths and thus moves the robot in the same way but is algorithmically different. D/sup */ Lite is simple, can be rigorously analyzed, extendible in multiple ways, and is at least as efficient as D/sup */. We believe that our results will make D/sup */-like replanning methods even more popular and enable robotics researchers to adapt them to additional applications.

We consider the problem of allocating a number of exploration tasks to a team of mobile robots. Each task consists of a target location that needs to be visited by a robot. The objective of the allocation is to minimize the total cost, that is, the sum of the travel costs of all robots for visiting all targets. We show that finding an optimal allocation is an NP-hard problem, even in known environments. The main contribution of this paper is PRIM ALLOCATION, a simple and fast approximate algorithm for allocating targets to robots which provably computes allocations whose total cost is at most twice as large as the optimal total cost. We then cast PRIM ALLOCATION in terms of a multi-round single-item auction where robots bid on targets, which allow for a decentralized implementation. To the best of our knowledge, PRIM ALLOCATION is the first auction-based allocation algorithm that provides a guarantee on the quality of its allocations. Our experimental results in a multi-robot simulator demonstrate that PRIM ALLOCATION is fast and results in close-to-optimal allocations despite its simplicity and decentralized nature. In particular, it needs an order of magnitude fewer bids than a computationally intensive allocation algorithm based on combinatorial auctions, yet its allocations are at least as good.

Motion-planning problems can be solved by discretizing the continuous configuration space, for example with graph-based or cell-based techniques. We study rapidly exploring random trees (RRTs) as an example of graph-based techniques and the parti-game method as an example of cell-based techniques. We then propose parti-game directed RRTs (PDRRTs) as a novel technique that combines them. PDRRTs are based on the parti-game method but use RRTs as local controllers rather than the simplistic controllers used by the parti-game method. Our experimental results show that PDRRTs plan faster and solve more motion-planning problems than RRTs and plan faster and with less memory than the parti-game method.

Robotics researchers have studied robots that can follow the trails laid by other robots. We, on the other hand, study robots that leave trails in the terrain to cover closed terrain once or repeatedly. How to design such ant robots has so far been studied only theoretically for gross robot simplifications. In this paper, we describe for the first time how to build physical ant robots that cover terrain. We show that a modified version of node counting can model the behavior of the ant robots and report on first experiments that we performed to understand their behavior better. These experiments confirm that our ant robots indeed cover terrain robustly even if the trails are of uneven quality, the ant robots are moved without realizing this, or some trails are destroyed. Finally, we report the results of a large-scale experiment where ten simulated ant robots covered a factory floor of 25 by 25 meters repeatedly over 85 hours without any ant robots getting stuck.

D* is a planning method that always routes a robot in initially unknown terrain from its current location to a given goal location along a shortest presumed unblocked path. The robot moves along the path until it discovers new obstacles and then repeats the procedure. D* has been used on a large number of robots. It is therefore important to analyze the resulting travel distance. Previously, there has been only one analysis of D*, and it has two shortcomings. First, to prove the lower bound, it uses a physically unrealistic example graph which has distances that do not correspond to distances on a real map. We show that the lower bound is not smaller for grids, the kind of map-based graph on which D* is usually used. Second, there is a large gap between the upper and lower bounds on the travel distance. We considerably reduce this gap by decreasing the upper bound on arbitrary graphs, including grids. To summarize, we provide new, substantially tighter bounds on the travel distance of D* on grids, thus providing a realistic analysis for the way D* is actually used.

We study how to coordinate a team of mobile robots to visit a number of given targets in a partially unknown terrain. Robotics researchers have studied single-item auctions to perform this exploration task but these do not make synergies between the targets into account. We therefore design combinatorial auctions, propose different combinatorial bidding strategies and compare their performance with each other, as well as to single item auctions and an optimal centralized mechanism. Our computational results in teambots, a multi-robot simulator, indicate that combinatorial auctions generally lead to significantly superior team performance than single-item auctions, and generate very good results compared to an optimal centralized mechanism.

In this paper, we describe a reactive robot architecture that uses fast replanning methods to avoid the shortcomings of reactive navigation, such as getting stuck in box canyons or in front of small openings. Our robot architecture differs from other robot architectures in that it gives planning progressively greater control of the robot if reactive navigation continues to fail, until planning controls the robot directly. Our first experiments on a Nomad robot and in simulation demonstrate that our robot architecture promises to simplify the programming of reactive robot architectures and results in robust navigation, smooth trajectories, and reasonably good navigation performance.

We analyze greedy mapping, a simple mapping method that has successfully been used on mobile robots. Greedy mapping moves the robot from its current location on a shortest path towards a closest unvisited, unscanned or informative location, until the terrain is mapped. Previous work has resulted in upper and lower bounds on its worst-case travel distance but there was a large gap between the bounds. In this paper, we reduce the gap substantially by decreasing the upper bound from /spl Oscr/;(|V|/sup 3/2/) to /spl Oscr/;(|V|ln|V|) edge traversals, where |V| is the number of vertices of the graph. This upper bound demonstrates that the travel distance of greedy mapping is guaranteed to be small and thus suggests that greedy mapping is indeed a reasonable mapping method. The guaranteed good performance of greedy mapping is robust in that it holds for different versions of greedy mapping, regardless of sensor type and sensor range.

Mobile robots often operate in domains that are only incompletely known, for example, when they have to move from given start coordinates to given goal coordinates in unknown terrain. In this case, they need to be able to replan quickly as their knowledge of the terrain changes. Stentz' Focussed Dynamic A* is a heuristic search method that repeatedly determines a shortest path from the current robot coordinates to the goal coordinates while the robot moves along the path. It is able to replan one to two orders of magnitudes faster than planning from scratch since it modifies previous search results locally. Consequently, it has been extensively used in mobile robotics. In this paper, we introduce an alternative to Focussed Dynamic A* that implements the same navigation strategy but is algorithmically different. Focussed Dynamic A* Lite is simpler, easier to understand, easier to analyze and easier to extend than Focussed Dynamic A*, yet is more efficient. We believe that our results will make D*-like replanning algorithms even more popular and enable robotics researchers to adapt them to additional applications.

Incremental heuristic search methods can often replan paths much faster than incremental or heuristic search methods individually, yet are simple to use. So far, they have only been used in mobile robotics to move a robot to given goal coordinates in unknown terrain. As far as we know, incremental heuristic search methods have not yet been applied to the problem of mapping unknown terrain. In this paper we therefore describe how to apply our incremental heuristic search method D* Lite, that combines ideas from Lifelong Planning A* and Focussed D*, to mapping unknown terrain, which is rather nontrivial. We then compare its runtime against that of incremental search and heuristic search alone, demonstrating the computational benefits of their combination. By demonstrating the versatility and computational benefits of incremental heuristic search, we hope that this underexploited technique will be used more often in mobile robotics.

In this paper, we introduce an efficient replanning algorithm for nonde- terministic domains, namely what we believe to be the first incremental heuristic minimax search algorithm. We apply it to the dynamic dis- cretization of continuous domains, resulting in an efficient implemen- tation of the parti-game reinforcement-learning algorithm for control in high-dimensional domains.

This article studies decision-theoretic planning or reinforcement learning in the presence of traps such as steep slopes for outdoor robots or staircases for indoor robots. In this case, achieving the goal from the start is often the primary objective while minimizing the travel time is only of secondary importance. This article studies how this planning objective interacts with possible representations of the planning tasks, namely whether to use a discount factor that is one or smaller than one and whether to use the action-penalty or the goal-reward representation. It is shown that the action-penalty representation without discounting guarantees that the plan that maximizes the expected reward also achieves the goal from the start (provided that this is possible) but neither the action-penalty representation with discounting nor the goal-reward representation with discounting have this property. The article then shows exactly when this trapping phenomenon occurs, using a novel interpretation of discounting, namely that it models agents that use convex exponential utility functions and thus are optimistic in the face of uncertainty. Finally, it is shown how the selective state-deletion method can be used in conjunction with standard decision-theoretic planners to eliminate the trapping phenomenon.

We study a greedy mapping method that always moves the robot from its current location to the closest location that it has not visited (or observed) yet, until the terrain is mapped. Although one does not expect such a simple mapping method to minimize the travel distance of the robot, we present analytical results that show (perhaps surprisingly) that the travel distance of the robot is reasonably small. This is interesting because greedy mapping has a number of desirable properties. It is simple to implement and integrate into complete robot architectures. It does not need to have control of the rebut at all times, takes advantage of prior knowledge about parts of the terrain (if available), and can be used by several robots cooperatively.

We show that finding localization plans with optimal worst-case execution time for localization tasks with short-range sensors in discretized domains is NP-hard, even within a logarithmic factor. This strongly suggests that finding and executing localization plans with optimal or even near-optimal worst-case execution time cannot be done in polynomial time. Greedy localization methods interleave planning and execution and keep the amount of planning performed between moves small. We analyze one such greedy localization method, the delayed planning architecture, and show that it can find and execute localization plans in polynomial time and thus substantially reduce the sum of planning and execution time compared to localization methods that find localization plans with optimal or near-optimal execution time. We also characterize how suboptimal the execution time of its localization plans can be. These results provide a first step towards analyzing other greedy localization methods.

Incremental search techniques find optimal solutions to series of similar search tasks much faster than is possible by solving each search task from scratch. While researchers have developed incremental versions of uninformed search methods, we develop an incremental version of A*. The first search of Lifelong Planning A* is the same as that of A* but all subsequent searches are much faster because it reuses those parts of the previous search tree that are identical to the new search tree. We then present experimental results that demonstrate the advantages of Lifelong Planning A* for simple route planning tasks. 1 Overview Artificial intelligence has investigated knowledge-based search techniques that allow one to solve search tasks in large domains. Most of the research on these methods has studied how to solve one-shot search problems. However, search is often a repetitive process, where one needs to solve a series of similar search tasks, for example, because the actual situation turns out to be slightly different from the one initially assumed or because the situation changes over time. An example for route planning tasks are changing traffic conditions. Thus, one needs to replan for the new situation, for example if one always wants to display the least time-consuming route from the airport to the conference center on a web page. In these situations, most search methods replan from scratch, that is, solve the search problems independently. Incremental search techniques share with case-based planning, plan adaptation, repair-based planning, and learning search-control knowledge the property that they find solutions to series of similar search tasks much faster than is possible by solving each search task from scratch. Incremental search techniques, however, differ from the other techniques in that the quality of their solutions is guaranteed to be as good as the quality of the solutions obtained by replanning from scratch. Although incremental search methods are not widely known in artificial intelligence and control, different researchers have developed incremental search versions of uninformed search methods in the algorithms literature. An overview can be found in [FMSN00]. We, on the other hand, develop an incremental version of A*, thus combining ideas from the algorithms literature and the artificial intelligence literature. We call the algorithm Lifelong Planning A* (LPA*), in analogy to “lifelong learning” [Thr98], because it reuses  We thank Anthony Stentz for his support. The Intelligent Decision-Making Group is partly supported by NSF awards under contracts IIS- 9984827, IIS-0098807, and ITR/AP-0113881. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the sponsoring organizations and agencies or the U.S. government.  information from previous searches. LPA* uses heuristics to focus the search and always finds a shortest path for the current edge costs. The first search of LPA* is the same as that of A* but all subsequent searches are much faster. LPA* produces at least the search tree that A* builds. However, it achieves a substantial speedup over A* because it reuses those parts of the previous search tree that are identical to the new search tree.

A popular technique for getting to a goal location in unknown terrain is planning with the freespace assumption. The robot assumes that the terrain is clear unless it knows otherwise. It always plans a shortest path to the goal location and re-plans whenever it detects an obstacle that blocks its path or, more generally, when it detects that its current path is no longer optimal. It has been unknown whether this sensor-based planning approach is worst-case optimal, given the lack of initial knowledge about the terrain. We demonstrate that planning with the freespace assumption can make good performance guarantees on some restricted graph topologies (such as grids) but is not worst-case optimal in general. For situations in which its performance guarantee is insufficient, we also describe an algorithm, called Basic-VECA, that exhibits good average-case performance and provides performance guarantees that are optimal up to a constant (user-defined) factor.

In this paper, we study how to traverse all edges of an unknown graph G = (V; E) that is bi-directed and strongly connected. This problem can be solved with a simple algorithm that traverses all edges at most twice, and no algorithm can do better in the worst case. Artificial Intelligence researchers, however, often use the following online nearest neighbor algorithm: "repeatedly take a shortest path to the closest unexplored edge and traverse it." We prove bounds on the worst-case complexity of this algorithm. We show, for example, that its worst-case complexity is close to optimal for some classes of graphs, such as graphs with linear or star topology and dense graphs with edge lengths one. In general, however, its complexity can grow faster than linear in the sum of all edge lengths, although not faster than log(V ) times the sum of all edge lengths. 1 Introduction In this paper, we study how to explore unknown environments that can be modeled as bi-directed graphs. Bi-directed gra...

Navigation methods for office delivery robots need to take various sources of uncertainty into account in order to get robust performance. In previous work, we developed a reliable navigation technique that uses partially observable Markov models to represent metric, actuator and sensor uncertainties. This paper describes an algorithm that adjusts the probabilities of the initial Markov model by passively observing the robot's interactions with its environment. The learned probabilities more accurately reflect the actual uncertainties in the environment, which ultimately leads to improved navigation performance. The algorithm, an extension of the Baum-Welch algorithm, learns without a teacher and addresses the issues of limited memory and the cost of collecting training data. Empirical results show that the algorithm learns good Markov models with a small amount of training data.

Reliable navigation is critical for a lunar rover, both for autonomous traverses and safeguarded remote teleoperation. This paper describes an implemented system that has autonomously driven a prototype wheeled lunar rover over a kilometer in natural, outdoor terrain. The navigation system uses stereo terrain maps to perform local obstacle avoidance, and arbitrates steering recommendations from both the user and the rover. The paper describes the system architecture, each of the major components, and the experimental results to date.